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M O V E O V E R OR H O W T O W I N A T D R A U G H T S
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By Derek Oldbury
BOOK ONE
INTRODUCTION
What do you think this is?
Every time you lose at draughts and ask what in blazes it is all about,
not a soul tells you where you can go to find out - even though William Payne
wrote the first English book 'Introduction to the Game of Draughts' in 1756.
Since then the game has been 'introduced' many times over, but never
explained.
Ask your friend who plays to lend you a good guide to the game (is it 'You
Too Can Win' or 'Never in a Huff'?). He will show you a book - and it looks
like a 'bus time-table or perhaps a losing system of betting on horses. You
point at the columns of symbols on page after page, and your friend says
that these are the best moves to play, neatly tabulated to make happy
reading. You ask, then, if all the best moves have been found, and your
friend says No. So you ask him how you will know when the book tells the
best move, or when there is really some other move that is better. Your
friend says you won't know (until you've lost a few games, keeping to the
book - that's experience), but that the author is a leading oracle on the
game. You ask how many titles this genius has won and your friend says that
actually none - but he often tells the Champions where they should have
moved, so he must know a lot.
You take one more look at the book, and you ask if there is no other way,
perhaps a few general principles - strategy and all that? You are repaid by
a blighting glance of scorn from your one-time friend. Principles! Don't you
know that draughts is so deep, so profound, so - there are no principles;
nobody has dared! What do you think it is - chess?
He goes on, but you don't listen. Not even when he quotes the beautiful
prose of Edgar Allen Poe which says that chess is kids' stuff compared to
draughts; nor when he tells you that Lady Hamilton used to show Lord Nelson
some good moves, 'twixt battles. You do not faint, even, when he divulges
that Rameses III played with Cleopatra, while the slaves built the Pyramids
around them, which is possibly not strictly true.
You are thinking it would perhaps be droll if you could know the idea
behind the game, the master scheme - for of course there must be one;
anybody can see that. If you knew, then you could give back the beatings
handed out to you by your clubmates. In your mind's eye you see them burying
their books in rage while you explain that it is just a matter of applying
the theory. But what theory? You could be Champion if you knew.
If only you knew.
CHAPTER ONE
I'm not related to Einstein
If you want to know about draughts it would not be best to begin at the
beginning. If you ask me to tell you the best move to start off your game
it is like saying 'Which is the best way to get there?' I reply 'Where?' and
you come back with 'Oh, just anywhere!' We would not get very far that way.
Even if I could say that this move is better than all others, come what may,
rain or shine, I have not told you why; so you would have to take my word
for it. Well, you do, and you are now on the second move of your game and
still in good shape - but as the final move is the one which will count (and
you know it) you are not very easy in your mind. Of course, you can ask me
again to say what is the best move, and the one after that, and maybe I could
play the whole game for you and you could go back to sleep. Let us try some
other angle.
Draughts is a duel, a battle of ideas. You win your game because your
ideas are better, stronger, than of those of him whom you play. This does
not mean that you have to be related to Einstein to be a draughts champion.
If you have an imagination, know the truth when you see it, and can keep a
straight face, then you are half-way there.
Now, ideas about draughts and probably almost anything else come from
knowledge, which you can get in two ways. By experience, or by thinking it
out for yourself. Many players will tell you experience is the only teacher;
and they will point with pride to the fact that they have put in some thirty
or forty years, amassing draughts lore. By the time I was in my late 'teens
I could usually take these experienced woodpushers and trim them down to
size in about half and hour. Even now, it is the really original player, the
one who has his own ideas about the game, who gives me the most trouble.
When you go into a fight, of any sort, a main concern must be the
battlefield, so to speak. It may be there are danger zones which you must
shun, into which you must seek to impel the foe: these should be known. It
may be there are key points which, seized, will control the whole sphere of
action and will let the course of events be dictated - by you, or by the
other player? If we take a look at the board se may get some ideas oj this.
You may think that looking only at an empty board will not tell you much
about the game - beyond the bare fact that, as draughts is played on all
squares of the same hue, all the moves and jumps are done in an obliqua
direction.
DIAGRAM 1
+------------------------+
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
+------------------------+
Look again, and note first that the squares are not all the same - those
in the centre of the board are very unlike those around the perimeter. From
the centre, it uses only a few moves to get to any square on the board; a
few steps and you are at the scene. It is a long way from one side of the
board to the other; by the time you get there it may be too late. Apart from
speed, the central squares offer a wider scope: from them you can assail or
uphold either flank, wherever there is the more profit. In some cases you
will switch your attack, or defence, from this flank to that; and usually
you will need to pass through the central squares. If these are in your
control you can carry out your plan; while if they are ruled by the foe your
communications are cut and your men may have to slink around the side-lines,
lurking in the shadows until in the end, alone, they are made away with.
Control of the centre can mean control of the board.
If the outer squares are less desirable, then of these the squares in the
very corners of the board will be even less so and in many cases they are
really unsafe. A boxer will not be pinned on the ropes if he can help it -
if he is held fast in a corner then he is in dire trouble.
The four corners of a draughts board are not identical. Two of them
consist of only one square with one exit from that square: these single
corners will as a rule be good places to stay away from. The double corner
squares protect each other, and with twin exits will be safe in contrast to
the single corners.
Now, all these remarks may give you the idea that by playing towards the
centre all the time you can step out along the winning path; but go not so
fast. That is the way to ruin. If you move all your men to the centre they
will only get in the way of each other and give rise to a jam. A tightly
packed group calls forth a pincer movement from the foe. Control is the
essential; you occupy the centre by as many men as will gain control, but no
more. You get control when your opponent is unable to move on to any of the
centre squares and so is forced into the less favoured areas of the board.
This is in fact your ultimate goal: to drive the enemy into the wilderness
where he shall perish. Central control is a means to this end.
We can stress this view of the board, by contrasting the action of a king
to that of a man. A king surveys the board in all directions, and the power
of a king may be felt near and far. Not so a man, which from the first sees
a vista rapidly waning in size and scope; at each step the range narrows,
the danger grows, and so often the short life is put out long ere there is
any chance to be a king. This is why it is not wise to let a man that is
well advanced come to be fixed on the side of the board; there it will be
cut off from comrades and be of no use, perhaps for the rest of the game,
and the time and effort spent in advancing it will have been wasted.
A chain of squares across the board forms an oblique line. Perhaps we can
call such lines diagonals - after all, that is what they are. As you will
soon see, there are seven diagonals. However, only one of them is quite
straight from end to end; that is the diagonal which extends from single
corner to single corner, thus:
DIAGRAM 2
+------------------------+
|::: ::: ::: ::: ^ |
| ::: ::: ::: ^ :::|
|::: ::: ::: ^ ::: |
| ::: ::: ^ ::: :::|
|::: ::: ^ ::: ::: |
| ::: ^ ::: ::: :::|
|::: ^ ::: ::: ::: |
| ^ ::: ::: ::: :::|
+------------------------+
It may be as well to estimate the nature of a diagonal you intend to
occupy or control. A diagonal may affect the power of a piece just as we
find a square to do. The most obvious effect that the single corner diagonal
has is that it cuts the board into halves, as it were. It divides your forces
from those of the foe. Seen from this angle, at the start of a game only
one of your twelve men is already in the enemy area; three are on neutral
ground. In playing an attacking game these men will be brought into action
with little delay, you may guess, and you will be right.
The single corner diagonal is the line of defence (we can call it the
D-line) that separates the two armies: to gain control of this line is to
take the initiative; to cross it is to begin the attack.
In the following set-up neither side takes any risks and control is
shared.
DIAGRAM 3
The D-line
+------------------------+
|::: ::: b ::: b ::: ^ |
| ::: ::: b ::: ^ :::|
|::: ::: b ::: ^ ::: |
| ::: b ::: ^ ::: :::|
|::: ::: ^ ::: w ::: |
| ::: ^ ::: w ::: :::|
|::: ^ ::: w ::: ::: |
| ^ ::: w ::: w ::: :::|
+------------------------+
If the single corner diagonal is defensive in character, then a line which
cuts across it and through the centre of the board must clearly be termed a
line of attack: any activity along this line signifies aggression. This is
the A-line.
In Diagram 5, the Blacks occupy their own A-line and in that way control
it. Whether they also control White's A-line will depend on the placing of
the White men, which I do not show. Wherever they are,
DIAGRAM 4 DIAGRAM 5
The A-line A-line control
+------------------------+ +------------------------+
|::: ^ ::: ::: ::: | |::: ::: ::: ::: |
| ^ ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ^ ::: ::: ::: | |::: ::: ::: ::: |
| ::: ^ ::: ::: :::| | ::: b ::: ::: :::|
|::: ::: ^ ::: ::: | |::: ::: b ::: ::: |
| ::: ::: ^ ::: :::| | ::: ::: b ::: :::|
|::: ::: ::: ^ ::: | |::: ::: ::: b ::: |
| ::: ::: ::: ^ :::| | ::: ::: b ::: b :::|
+------------------------+ +------------------------+
one thing is plain - they cannot be on the like squares on White's side of the
the board, as both armies cannot be attacking at the same time along their
own A-line. In other words, the player who first engages in an A-line attack
takes the lead. The opponent must reply in some other way.
In both Diagrams 3 and 5, did you notice the extra man at the base? Though
this man takes no active part in commanding the diagonal yet the added
strength is desirable, for it is the base which the opponent will attack.
If the base can be destroyed the whole structure may break up.
It is here that we have the case for the squares at the outer edges of the
board. A man on such a square is immune from direct 'capture' (the word often
used by draughts players to denote a jump; yet the act of leaping over an
enemy piece surely symbolizes 'over thy dead body' - but this is by the
way). A man at the edge of the board is in a position to support other men
which may form a chain of some power. A strong player will in this way
transform into a weapon what might have been a defect.
I clarify this point because it is one about which most tyros are hazy -
and very few self-styled experts are able to enlighten them on it.
The A and D diagonals are the major lines of attack and defence. You
expand the power and scope of your men when you fill and control vital lines
with them, so it is, of course, this you will try to do.
The diagonal which runs this side of the A-line has by contrast much less
import; for the greater part of its length points to the side of the board.
It's best squares are those at the edges, which may be used to support more
active pieces. The B-line (the name comes easily to it) is a diagonal with
weaknesses, which a clever opponent will often make use of for his own ends.
One of the more potent ways is for the foe to place a man on the square
which intersects your D- and B-lines, dominating both and undermining your
A-line also. Beware of danger at the spot marked X!
Most of the C-line runs towards the centre and so it is stronger than the
nearby B-line, and as also this part of the C-line intersects the attacking
A-line it can be termed an important diagonal. I need hardly say that the
square at which the A- and C-lines meet and cross is of great value in
formational play, both in attack and in counter-attack. It is a key square,
and now you know why.
DIAGRAM 6 DIAGRAM 7
The weak B-line The C-Line
+------------------------+ +------------------------+
|::: ::: ^ ::: ::: | |::: ::: ::: ^ ::: |
| ::: ^ ::: ::: :::| | ::: ::: ^ ::: :::|
|::: ^ ::: ::: ::: | |::: ::: ^ ::: ::: |
| ^ ::: ::: ::: :::| | ::: ^ ::: ::: :::|
|::: ^ ::: ::: ::: | |::: ^ ::: ::: ::: |
| ::: x ::: ::: :::| | ^ ::: ::: ::: :::|
|::: ::: ^ ::: ::: | |::: ^ ::: ::: ::: |
| ::: ::: ^ ::: :::| | ::: ^ ::: ::: :::|
+------------------------+ +------------------------+
The lines E and F are for the most part defensive, supporting as they do
activity along the D-line. This is their main utility.
DIAGRAM 8 DIAGRAM 9
The E-line The F-line
+------------------------+ +------------------------+
|::: ::: ::: ^ ::: | |::: ::: ^ ::: ::: |
| ::: ::: ::: ^ :::| | ::: ::: ^ ::: :::|
|::: ::: ::: ::: ^ | |::: ::: ::: ^ ::: |
| ::: ::: ::: ^ :::| | ::: ::: ::: ^ :::|
|::: ::: ::: ^ ::: | |::: ::: ::: ::: ^ |
| ::: ::: ^ ::: :::| | ::: ::: ::: ^ :::|
|::: ::: ^ ::: ::: | |::: ::: ::: ^ ::: |
| ::: ^ ::: ::: :::| | ::: ::: ^ ::: :::|
+------------------------+ +------------------------+
If you look at Diagram 3, you will see that both sides occupy their
E-lines, and this is a typical set-up.
Ending our alphabetical trip along the diagonals, we arrive at G:
DIAGRAM 10
+------------------------+
|::: ^ ::: ::: ::: |
| ::: ^ ::: ::: :::|
|::: ::: ^ ::: ::: |
| ::: ::: ^ ::: :::|
|::: ::: ::: ^ ::: |
| ::: ::: ::: ^ :::|
|::: ::: ::: ::: ^ |
| ::: ::: ::: ^ :::|
+------------------------+
The fact that the G-line has almost all the features of the A-line tempts
one to regard it as a line of attack, until we realise that what is our
G-line is also the opponent's A-line. Any attacks along this line may be
expected to stem from the opposite side of the board rather than from our
side. However, if we first set up a strong formation along our A-line then
an attack along the G-line can be effectual, thus:
DIAGRAM 11
+------------------------+
|::: ^ ::: ::: ::: |
| ::: ^ ::: ::: :::|
|::: ::: ^ ::: ::: |
| ::: b ::: ^ ::: :::|
|::: ::: b ::: ^ ::: |
| ::: ::: b ::: b :::|
|::: ::: ::: b ::: b |
| ::: ::: b ::: b :::|
+------------------------+
Here, Black advances two men along the G-diagonal, with the powerful
support of the formation shown before, at Diagram 5. This is about the best
way to conduct a G-line attack.
In general, an advance early in the game along the G-line serves only to
forestall enemy activity and is a defensive measure. In Diagram 12 below,
Black has thrown away the natural advantages of having the right to move
first and so make the first threat, and here plays for safe defence.
DIAGRAM 12
+------------------------+
|::: w ::: w ::: w ::: w |
| w ::: w ::: w ::: w :::|
|::: w ::: w ::: ::: w |
| ::: ::: w ::: :::|
|::: ::: ::: b ::: |
| b ::: b ::: b ::: b :::|
|::: b ::: b ::: b ::: |
| b ::: b ::: b ::: b :::|
+------------------------+
Around the early nineteenth century, most of the leading Masters thought
that starting off a game in such a way as this would give Black a weak
formation. Most of the moderns consider it a good method of opening. This
may seem just another case of the light of present-day knowledge illumin-
ating the dark ages. Not so. The truth is that the old-timers held a view
of the word 'weak' not at all like that of the modern players. To them, a
weak opening was one which promised few chances of getting a win, though it
might be safe enough merely to get a draw - weakness denoted lack of opport-
unity rather than danger - the nineteenth-century players thought the proper
aim in playing draughts was to win the game. Nowadays, the view is that the
player should first and foremost play to avoid defeat, that is to say, play
for a drawn result. Of course, if an opportunity to win should appear (and
it IS by chance) then go for it, but keep the draw in sight at all times.
To the modernist then, an opening is not weak if it is safe for a draw, even
though it may offer virtually no chances to win.
My money is on the old-timers in this. I play the game to win. I make the
chances. I win all the games I can, and I do not wait for chances to win. I
make the chances. Maybe that is why I am Champion. However, I have the
perfect system for anybody who wants to become unbeatable at the game, and
it is this. Do not play. Then you can't lose.
If we now sum up our survey of the squares and diagonals, we must come to
see very clearly that as the squares often determine the value of the
pieces, so the action of the pieces as a whole may determine the character
and strength of the diagonals - a diagonal is strong because it allows the
build-up of telling formational patterns. It might be useful to state
generally that, early in the game, when we have available numbers of men to
form chains of attack or defence, then the diagonals are of paramount
importance. Late in the game, when forces are dwindling to a few scattered
units, then the individual squares come into their own.
To master these features of the board is a basic 'must' in pursuing a
grasp of the mysteries of the game. You can hardly overdo this, you cannot
know your board too well. Whatever plans you may conceive, however grand the
scale, if they do not take into account the contours of the field of battle
then they will not work out. The successful boxer knows how to use the ring.
You must know how to use the board.
Here is a composite picture of the seven diagonals, seen from the point of
view of each player. Study this well.
DIAGRAM 13 DIAGRAM 14
As he sees it
+------------------------+ +------------------------+
8 |:::AG :::BF :::CE ::: D | |:::AG :::BF :::CE ::: D | 1
7 | A :::BG :::CF :::DE :::| | G :::AF :::BE :::CD :::| 2
6 |:::AB :::CG :::DF ::: E | |:::FG :::AE :::BD ::: C | 3
5 | B :::AC :::DG :::EF :::| | F :::EG :::AD :::BC :::| 4
4 |:::BC :::AD :::EG ::: F | |:::EF :::DG :::AC ::: B | 5
3 | C :::BD :::AE :::FG :::| | E :::DF :::CG :::AB :::| 6
2 |:::CD :::BE :::AF ::: G | |:::DE :::CF :::BG ::: A | 7
1 | D :::CE :::BF :::AG :::| | D :::CE :::BF :::AG :::| 8
+------------------------+ +------------------------+
As you see it
CHAPTER TWO
My girl friend has 'it'
It would be a good idea now to get to know the power of the pieces. If I
show you how to carry out some simple ideas, and you learn to execute them
quickly and easily, that will be as good a way as any. You will benefit from
this type of practice, just as an athlete performs exercises to develop
strength and a smooth action.
One of the vital concepts of the game is that you do not always make a
move because you wish to, but at times because you have to; it is your turn
and you must move somewhere. If it is your turn and you cannot, then you
have lost the game. That is what decides your fate, nothing else.
Consider the positions in Diagrams 15 and 16.
In both cases the telling factor is, whose turn it is to move. In all
other respects the positions are equal. Each player will advance his king
towards the centre until it confronts the opposing king, thus checking it's
progress. At that instant the king whose turn it is will be forced to yield
ground and make way for the advancing enemy.
DIAGRAM 15 DIAGRAM 16
+------------------------+ +------------------------+
|::: B ::: ::: ::: | |::: ::: ::: ::: B |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: ::: ::: W :::| | W ::: ::: ::: :::|
+------------------------+ +------------------------+
In the first example, the king must retreat to the double corner for
safety; in the second example there is no escape and the king is pressed
back to the edge of the board and there held fast. In both cases the king is
put to flight because, and only because, the move is against him.
When a player is able to check the action of an opposing king or man in
this way he is said to have 'the move'. This is meant in much the same way
as you might say your girl friend has 'it', meaning that she has sex-appeal.
That is not everything but it contributes.
Let us see another example. Observe Diagram 17.
DIAGRAM 17 DIAGRAM 18
White - to play White - to play
+------------------------+ +------------------------+
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: w ::: ::: ::: | |::: ::: ::: B ::: |
| ::: ::: B ::: W :::| | ::: ::: ::: W :::|
|::: ::: ::: ::: | |::: ::: w ::: ::: |
| ::: ::: ::: :::| | ::: b ::: ::: :::|
|::: b ::: ::: ::: | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
+------------------------+ +------------------------+
Black Black
It is White's turn and he is lost. It is clearly of no use to move the
king and so the man must advance down the board, along the G-line, only to
be met by the opposing Black man. In trying to push his way through, White
permits Black to offer a choice of exchanges (Diagram 18). Whichever jump
White chooses, 'the move' is against him and he is soon driven to the danger
zones of the board.
Some persons hold the notion that if one player does not have 'the move'
then the other player has it; that is to say, 'the move' is a thing present
at all times during a game. This is not so, for 'the move' is no more than
the effect of confining enemy manoeuvres in the specific manner which I have
described. In any fluid situation, wherein both sides have free action, 'the
move' does not exist for either player. The mistaken idea of the omnipres-
ence, so to speak, of 'the move', led early writers on the game to publish
curious systems of computing - by which the player would be able to tell at
all times whether Black or White held 'the move'. Some of these efforts
remind one of the ancient alchemists' formula for the elexir of life (take
three goblins and stir well) and are about as fertile. Most of these miscon-
ceptions came about through confusing 'the move' with something else -
which we shall examine in detail later on.
Meanwhile, some more simple positions:
DIAGRAM 19 DIAGRAM 20
+------------------------+ +------------------------+
|::: ::: ::: ::: | |::: ::: ::: ::: |
| B ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: B ::: W ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: B ::: :::|
|::: ::: ::: ::: | |::: ::: ::: B ::: |
| ::: ::: ::: :::| | ::: ::: ::: W :::|
+------------------------+ +------------------------+
From Diagram 19, Black begins by driving the White king to the double
corner. This is done by making a 'waiting' move with the free king and then
using the power of 'the move' to push the White king along. When this has
been done the free king is then brought to the scene of action. By this time
you will have the position shown on Diagram 20 and it will be White to play,
where he has no choice but to allow Black to enter the double corner and
thus drive him out - on the very scientific maxim that no two objects may
occupy the same point in space. The rest is easy.
If two free kings can dispose of one king, then three versus two should
simply be a matter of exchanging one for one, so reducing the situation to
that we have just seen - and so it is.
DIAGRAM 21
+------------------------+
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: W ::: B ::: ::: |
| ::: ::: B ::: :::|
|::: ::: ::: B ::: |
| ::: ::: ::: :::|
|::: ::: ::: W ::: |
| ::: ::: ::: :::|
+------------------------+
Black to play and win
To do this, from Diagram 21, Black must bring about either of the positions
shown below:
DIAGRAM 22 DIAGRAM 23
White - to play White - to play
+------------------------+ +------------------------+
|::: ::: ::: ::: | |::: W ::: ::: ::: |
| W ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: B ::: ::: ::: |
| ::: B ::: ::: :::| | ::: ::: ::: :::|
|::: ::: B ::: ::: | |::: ::: B ::: ::: |
| ::: ::: B ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: B ::: W |
| ::: ::: ::: W :::| | ::: ::: ::: :::|
+------------------------+ +------------------------+
Black to win Black to win
In each of these, White will be compelled - at his next move - to permit
the exchange Black seeks.
Now I have given you only brief explanations to the various examples
treated in this chapter, and for two reasons. Firstly, the more you can work
out for yourself the quicker progress you will make and surer grasp you will
develop; secondly, in playing over these positions with only the general
idea to guide you, you will learn to make series of moves to fit into a
pre-conceived scheme. At the moment, it is only a scheme which someone else
has outlined to you, but later on you will design your own. You will no
longer consider things in a disconnected sort of way, but as a general maps
out a campaign.
I end this chapter with a position which illustrates again some of the
points touched upon so far in our discussion. You might use it to test
yourself, to see if all is clear to you. If the solution eludes you then it
might be as well to re-read a bit rather than plunge onwards and risk
confusion. That is up to you.
DIAGRAM 24
Study by Oldbury
White - to play
+------------------------+
|::: ::: ::: ::: W |
| w ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: ::: ::: B ::: |
| b ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
+------------------------+
Black - to win
CHAPTER THREE
But - can it use it's legs?
'This book defines what the game is - and tells it straight.' Thus spake
Julius D'Orio of his own 'Mysteries of Dama'. Not a bad idea.
If a scientist (not related to Einstein) were to tell it straight he might
expound along these lines: Draughts, being a compound of board, pieces, and
moves, may be reduced to the simple elements of space, force, and time. The
game is played in these elements, and gains or losses made in space, force,
or time are the sole means of deciding the game.
He would go on to define gains and losses in each of the three elements so
that we may identify them and also measure their degree. We could then
examine any position and make an accurate assessment, somewhat after this
style:
Space: Advantage to Black 33%
Force: : : White 16%
Time: : : Black 5%
Balance of power to Black 22%
If you are playing the Blacks in such a position and it is your turn, then
clearly all you have to do is to find a move to keep the balance of power
still at 22 per cent in your favour. It will be a matter of simple adding
and subtracting, and you will wait for your opponent to make some move that
will increase your ratio of power. No doubt our scientist friend will also
inform us of the exact degree at which a position goes 'over the top' and
becomes a win, say at 66 per cent.
Now it would be very nice if we could add up points in this way and arrive
at the truth of a situation, but we can't - at least, it would not be the
whole truth.
You observe a racehorse in the paddock, before the big race; you note the
fine limbs, the powerful quarters, and you resolve to trust this handsome
fellow with some of your hard-earned cash - it has all the 'points'. Yet the
question is not, has it an honest face - but, can it use it's legs. Alas,
you find it cannot, and you discover certain truths of which you were not
previously aware (you utter some of them, perhaps). One of these truths is
that an object in motion may shed qualities which in repose it seemed to
possess. There is, if you like, an 'X' factor which may not show until after
the event, when it is too late. In draughts, this is because at times the
moves have meaning only as part of a series; taken as isolated moves they
have no scientific basis, but their power as an integrated design sweeps
aside all other considerations. There is in the game artistic truth besides
scientific truth. We must seek both.
For instance, at the very start of a game the forces are equal and
scientific truth says, therefore, that a properly played game should end in
a draw. However, artistic truth tells us it should end in a win, for that
player who has the greater creative ability. If a player cannot accept both
these propositions then he will find it difficult to develop his skill to
any extent.
I think we may take it as read that an advantage in space or in force will
not be hard to assess, at least in a loose sort of way to begin with - it
will simply be a matter of counting squares and pieces. The concept of time,
in draughts, is less easy to grasp straightaway, as it has many facets. To
have the initiative is an advantage in time. To have 'the move' is also an
advantage in time.
Consider Diagram 25.
DIAGRAM 25
Black - to play
+------------------------+
|::: ::: b ::: b ::: b |
| b ::: ::: b ::: :::|
|::: ::: b ::: b ::: |
| b ::: w ::: b ::: b :::|
|::: w ::: w ::: b ::: w |
| ::: w ::: w ::: :::|
|::: ::: w ::: ::: w |
| w ::: w ::: w ::: :::|
+------------------------+
White wins
As the two armies are in identical patterns there is absolute equality in
space and in force. Yet if you will play out the position you will see that
Black is lost, and in a very few moves, as White has only to play along his
F-line to block up the foe altogether. This is an example of 'the move' in
what may be termed a pure sense. In examples from Chapter Two, having 'the
move' led to gains in other elements, by compelling the enemy to retreat to
inferior regions (gain in space) which in turn led to final extinction (gain
in force). Here, a win is realized by 'the move' alone - the respective
Black and White armies are still equal in every other way at the end.
There is another important aspect of time. Every move made by a man brings
it that much nearer a desirable goal, that of being promoted to the rank of
king. A man attains this state and so develops greater power and scope. Our
position may be said to be fully developed when all our men have reached the
king-row. In these terms, then, the degree of development we have made can
be estimated simply by the distance at which our men are from the king-row.
At the start of a game your twelve men stand at the three horizontal lines
(ranks) furthest from the king-row. There are eight such ranks, and the
eighth rank is the king-row. If you wish to assess the 'time value' of your
position and translate it into a number for easy reference, this can be
done. Simply count 1 for each of your men on the rearmost rank or base-line;
count 2 for each man on the second rank, 3 for each on the third - and so on
until you have counted all your men. Thus, before a game begins, your 'time
count' is 24, as it is also for your opponent who makes a separate count of
his own men.
Each move takes a man to a higher rank until it arrives at the eighth,
where it is crowned; the time value of a king will be 8. If we compare a
time-count taken of our own pieces with a count of the opponent's, the
higher number will tell us which side, Black or White, is nearer complete
development (100 per cent kings), and by how many moves.
We will try this out, from Diagram 26:
DIAGRAM 26 DIAGRAM 27
British Championship, 1952
White (Crabbe) White
+------------------------+ +------------------------+
|::: ::: ::: w ::: w | |::: ::: ::: w ::: w |
| ::: ::: ::: w :::| | ::: ::: ::: w :::|
|::: w ::: ::: ::: | |::: w ::: ::: ::: |
| ::: w ::: w ::: :::| | ::: ::: w ::: :::|
|::: ::: ::: w ::: | |::: b ::: ::: ::: |
| b ::: ::: ::: b :::| | ::: b ::: ::: b :::|
|::: ::: b ::: b ::: b | |::: ::: ::: b ::: b |
| b ::: ::: b ::: :::| | ::: ::: ::: :::|
+------------------------+ +------------------------+
Black (Oldbury) to play Black
Even without a count, a glance shows us that Black has made very little
progress and all his men are confined to the three lowest ranks. He has 2
men on the first rank, 3 on the second and 2 on the third: time-count = 14.
White is very much further advanced; with 2 men on his first rank, 1 on his
second, 1 on his third, 2 on his fourth and 1 on his fifth: a total of 20.
White then is 6 moves ahead in his development. As he also appears to
dominate the centre, and the forces are equal, a superficial analysis may
conclude that Black is in a bad way.
The game went on, and after my next four moves (which to the spectators, I
may add, seemed feeble and pointless) the position became that of Diagram
27. If we make a time-count we discover quite easily, but to our surprise,
that Black now has 2 men on the second rank, 2 on the third and 1 on the
fourth - total 14 - against which White now has 2 men on his first rank, 1
on his second, 1 on his third and 1 on his fourth - a count of only 11 in
all! Black now leads by 3 moves in contrast to trailing by 6 moves. Over a
short span of four moves Black in some way has managed to 'gain' 9 moves in
development. Has White been moving backwards?
Well, if you examine very closely these two positions you will see how
the change came about. It will be best if you find out this for yourself,
though I shall be going into this in more detail later on. Meanwhile it is
interesting to observe that the manoeuvre which led from Diagram 26 to
Diagram 27 also revealed the truth of the situation - the unguarded man
White has in the centre, which is now isolated and subject to attack. Black
soon brought pressure against this weakness and went on to win the game,
when White failed to find an adequate defence.
It is natural to ask now whether positional superiority and advanced
development go hand in hand. At this stage I would simply ask you to note as
a general, but not specific, guide: in the latter part of a game to be ahead
in development is an advantage in time; early in the game, to be ahead in
development is a disadvantage in time.
This is so, because at the end-game we aim towards well-defined object-
ives, for instance, possibly to promote a man to king and then to place it
on a vital square - the opponent has in view a similar plan and being ahead
in development may mean getting in first. Conversely. in the opening one of
our main concerns is to gain freedom of action for our forces- and on a board
which at that moment contains more occupied squares than vacant squares.
We have at our command a limited number of moves in so crowded an area, and
if we develop too rapidly there is a distinct danger of using up all our
resources - at best we will be embarrassed for a satisfactory move; at worst
we may even be blocked up , as in Diagram 25. Without being too precise, it
should help the student if he realizes that with, say, 10 men each side still
on the board, being 4 moves ahead in development would be enough to lose the
game, unless offset by considerable gains in space. With 11 men a side such
over-development would be fatal regardless of any gains in space.
In the diagram below, Black faces a dilemma:
DIAGRAM 28
White
+------------------------+
|::: w ::: w ::: w ::: w |
| w ::: w ::: w ::: w :::|
|::: ::: ::: w ::: w |
| w ::: ::: ::: :::|
|::: b ::: b ::: ::: |
| ::: ::: b ::: b :::|
|::: ::: b ::: b ::: b |
| b ::: b ::: b ::: b :::|
+------------------------+
Black - to play
Black has the unenviable choice of inferiority in any one of the three
elements. In time, if he permits the exchange which White seeks (Black is
already 2 moves ahead and this would make it 4 - try it); in force, if he
advances the man threatened, (White could soon cut it off); or in space, if
he covers up the threat (his single corner would then become very cramped).
We shall not discuss here the best way for Black to meet these problems, as
I have made my point - which is, that from the very first moves of a game
the issues of space, force, and time will confront you and demand to be
solved.
Your success across the board will depend upon how you face the challenge
of the elements.
CHAPTER 4
Now you come in for the kill
Up to now my main theme has been to reply to your question which began with
this book; yet in doing so many principles underlying the game have been
tossed lightly around, and you will be eager to set up the board and men,
ready to take on all who dare.
We have arrived at a point where a theory of draughts can be stated in
simple terms. The situation is assessed and then is formed a plan of action.
Thus the essential processes are to observe and then visualize.
Unfortunately for them, most players I meet seem to put the cart in front
of the horse, as it were, and they expend much energy in trying to visualize
the possible consequences of moves which I have not the least intention of
making - because these moves have no bearing on the situation in hand. As a
result, some of these players develop the ability to 'see' a fantastic
number of moves ahead - but of course if they are looking in the wrong
direction then that cannot help them an awful lot. If a plan is to have any
real basis it must be related to the facts of the present situation. The
more accurately these facts can be weighed up then the more effectively are
we able to plan.
In creating the concepts of space, force, and time we have forged the
tools with which we may gauge the value of a position as a whole, and also
pin-point the means by which we are to exploit its specific features.
Let us try our hand at this.
DIAGRAM 29
Study by 'F.T.V.'
White
+------------------------+
|::: ::: ::: ::: w |
| ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: ::: B ::: B ::: |
| ::: ::: ::: :::|
|::: ::: ::: ::: W |
| ::: ::: ::: :::|
+------------------------+
Black
Barely more than a casual glance is needed to reveal that Black is
decidedly superior in all three elements: with two kings versus a king and a
man (superior in quality if not in quantity), 7 moves ahead in development,
and undisputed control of the centre. When you learn also that White is to
play and you see that 'the move' is against him, you will be happy to have
the blacks.
Very well: your opponent moves his king across the double corner, and he
awaits your attack. You are ready to pounce.
You are considering what to do - and you make a disturbing discovery. No
matter where you move next you will still have the same degree of strength
that you have now; it neither grows nor diminishes! There is nothing to
differentiate between the eight possible moves at your disposal. How then
are you to select the best from them?
You suffer a bit of a shock; yet on reflection it becomes evident that this
is only what one would expect, and for two reasons. In the first place,
there must be thousands of different positions in which one side holds the
advantage in all of the elements, therefore that state alone cannot
possibly indicate actual moves which are to be made. Secondly, in any
situation wherein one side has complete control it is logical that the
stronger side should enjoy considerable freedom of action. An experienced
player will often use this natural positional advantage, and will tack
around, probing varying possibilities and getting the feel of the situation
before committing himself to a positive line. Then, when he is satisfied
that he has it all weighed up he comes in for the kill. This, as you may
well appreciate, is one good reason why having the advantage in all three
elements is a condition to be desired and to be sought.
Let us return to Diagram 29 and examine it in more detail, as it is
evident that we must. After all, we must never lose sight of our ultimate
objective which is to weaken and destroy the enemy; unless our present
seeming power is a means to that end it is of no great interest and much
over-rated as a guide to our prospects.
The first feature that attracts the attention is that Black cannot
increase his advantage in time, as he has already achieved '100 per cent
kings' and also has 'the move'. Any changes in the element of time must
favour White. Next, you will observe that as pieces which are at the edges of
the board cannot be jumped, White is in no immediate danger of losing
material. We see then, that though Black's pull in time and in force is real
enough, it is in neither of these elements that the attack will be carried
out. Black will operate in space.
The Black advantage in space here is very clear, as White's pieces are
extremely limited in scope. The purpose of the attack will be to limit it
still more. How may this best be done?
Now I am going to assume that you have read with care Chapter One, and that
you now have a good idea of the value of the various squares; at least
insofar that you appreciate that White will not advance his man except under
compulsion because, as you already know from Chapter One, each move made by
a man reduces its field of action. Of course, on the other hand, each move
brings the same man nearer the king-row but in a position such as that of
Diagram 29 the prospects of getting through, with two kings barring the
route, are at present very remote. Black will endeavour to encourage or
compel the White man to come forward.
The means to do this may readily be seen if the position of the White king
is examined. At the moment it seems safe enough; the king can move from side
to side and so long as it can move all is not lost. Yet we know, from
Diagrams 19 and 20, that the lone king is not in fact safe when opposed by
two kings.
Does not the plan now take definite shape? You will ignore the man and
attack the White king, with the threat to tie it up with your two kings.
When the White king is immobilized the man will have to advance - 'the move'
is against White and he must move somewhere. You will repeat your attacks on
the White king and so compel the man to move again and yet again. It is not
difficult to envisage these manoeuvres leading to a position such as we see
in Diagram 30:
DIAGRAM 30
White - to play
+------------------------+
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: ::: B ::: B ::: w |
| ::: ::: ::: :::|
|::: ::: ::: ::: W |
| ::: ::: ::: :::|
+------------------------+
Black
Nothing has changed except that the man has come to the fifth rank, yet
the end is very near. White to play cannot withstand even one more onslaught
against his king; as now the man is being made to assist in the attack and
is hampering the movements of its own king. In but a few more moves White
will have no choice but to give up the man in an effort to prolong the life
of the king.
Thus will Black gain a decisive advantage in the element of force by
exploiting his superiority in space, yet also giving up a part of his
superiority in time (development). It is in this way that the interplay of
the elements is seen and it is in the exact judgment of their merits at a
given moment that the niceties of the game are disclosed.
You have evaluated your position and have formed a plan by which you can
expect to win. However, it must be kept in mind that up to this stage you
have considered the situation only from your own point of view.
I may surprise you when I tell you that this is just as it should be. If a
player were to consider too deeply what reply the opponent may or may not
make to each of his own moves, then it would become impossible to think out
a coherent series of manoeuvres and no plans would ever be made. If you have
assessed the position at its proper ralua you are then ready to construct a
plan and carry it through and nothing the opponent can do can stop you.
This does not mean that we can afford to ignore our opponent's moves; it
does mean that we can bring them into proper perspective. While his moves
should not affect our plan they may well affect the actual way in which the
plan is to be carried out. For instance: you observe a certain weak spot in
the enemy structure and you resolve to attack in that direction. Your
opponent may choose to contest the issue, in which case you bring all
available pressure to bear on that point. Alternatively, he may elect to let
it go in your favour and meanwhile he will counter-attack elsewhere. In that
case you will adopt different tactics; you will attack the weakness, but
with a lesser force, keeping reserve material to meet your opponent's
intended counter-attack. Now in both cases you will attack the point which
from your survey you have decided is vulnerable, yet your method of proced-
ure will vary in accordance with the needs of the situation.
At Diagram 29 it would appear that White has very little to plan for, and
of course the position is a win for Black as we have already seen. If White
recognizes this, then his proper plan will be to make it as difficult as he
can for Black to win. If he does only this then his plan may quite properly
be said to have succeeded; the fact that Black wins does not alter this, as
I hope you see.
White's defensive plan will in general entail holding back the advance of
his man as long as is possible or practicable. This is to be expected, for
it is Black's scheme in reverse, yet it is not wholly a negative approach to
matters, as Black will soon find out. From Diagram 29 Black begins the
attack on the White king, threatening to drive it from the double corner, on
the assumption that White will advance his man rather than let that happen.
It comes as a mild surprise then when White continues to move the king and
suffers it to be pushed out, so:
DIAGRAM 31
White
+------------------------+
|::: ::: ::: ^ ::: w |
| ::: ::: ::: ^ :::|
|::: ::: ::: ::: ^ |
| ::: ::: ::: :::|
|::: ::: ::: ::: W |
| ::: ::: B ::: :::|
|::: ::: ::: ::: B |
| ::: ::: ::: :::|
+------------------------+
Black - to play
White's objective is now apparent. The man, though it stands in the weak
single corner, has the effect of 'enlarging' it in such a way that for
practical purposes it is now a 'triple corner' comprising three squares. The
White king, if able to reach this triple corner will in fact be much safer
here than in the double corner; the Black kings would be quite unable to
dislodge it from this haven and the result would be a draw.
This is a dramatic example of how, in addition to the squares determining
the value of the pieces, so also may the pieces radically alter the worth of
the squares.
From Diagram 31, it is evident that Black must cut off the White king's
flight and must compel it to return to the double corner. You may wonder at
this as it seems Black is merely going back on his tracks and will make no
headway. Look at Diagram 32:
DIAGRAM 32 DIAGRAM 33
White - to play White
+------------------------+ +------------------------+
|::: ::: ::: ::: w | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: x ::: |
| ::: ::: ::: :::| | ::: ::: B ::: :::|
|::: ::: B ::: ::: | |::: ::: ::: y ::: w |
| ::: ::: ::: :::| | ::: ::: ::: W :::|
|::: ::: ::: W ::: B | |::: ::: ::: z ::: |
| ::: ::: ::: :::| | ::: ::: ::: B :::|
+------------------------+ +------------------------+
Black Black - to play
A close survey will reveal that this is simply another case of pieces
changing the value of squares. By entering and occupying the double corner,
Black has in effect transformed it into a single corner! It is clear now why
the White king was not over-anxious to stay in this area. Either now or on
his next move White must begin moving his man. Actually, it will be better
to move it now - in the hope that while the two Black kings are separated
White may find an opportunity to rush his king to the other double corner;
both Black kings would need to give chase, which would let the White man
slip through to the king-row, unnoticed as it were. I should add that Black
would have to play rather carelessly to allow this escape, yet White loses
nothing by trying.
Assuming best play on both sides, eventually Diagram 33 is formed, and
much progress has been made. You have forced the White man to the fifth rank
and it remains only to combine your two kings for the final attack.
Throughout the operations from Diagram 31 one of your kings has stayed
within the double corner, now it must be brought out. This is done quite
easily. You make a waiting move with your free king, to the square marked X;
White must reply to square Y to stall off this king, this enables you to
play your other king to Z. The White king goes back into the double corner
and your kings are both free. It will need only a very short while to reach
Diagram 30, your original target, and so Black wins.
It is thus we come to realize that by close observation we are able to
make our assessment of a position and therefrom construct an overall plan or
method of play. We see also that while success will hinge upon the
conception of a plan that is appropriate to the circumstances, and that it
must be thought out in its entirety in advance, yet the details of its
execution may to some extent be adapted to meet specific manoeuvres from the
foe.
Most vital of all, we realize that every move we make must have a motive,
either in its own right or as part of a series. You do not find reasons to
fit moves - you find moves to fit reasons. That is my system.
*
B O O K 2
I N T R O D U C T I O N
Start now
The value of any theory lies in its application, or, the proof of the
pudding is in the eating. However one says it, you will now wish to see how
my system works out; and so we shall examine a variety of critical
situations, with this in view. In learning to estimate the worth of a
position by synthesis you are at the same time evolving the true analytical
ability so needful to success.
I say 'true', for there are in the game many self-styled 'analysts' whose
only means of assessing a position is to push the men to and fro, moving
this way and that on a sort of trial and error basis - until such time as
they are heartily sick of the whole thing, whereupon they publish what
little they have discovered under the bold pretext of having 'analysed' the
situation. If this is analysis, then scratching the back of my neck is
scientific research.
I must warn you very strongly against this attitude of thinking which
says, 'I'll try this move; after all, if it turns out bad I can always try
the other next time.' In a game like draughts, in which there are millions
of varying positions that can arise, there is no concrete reason why you
should ever play the same game twice in your life. Hence, you may never get
a second chance to try this or that - the only chance you had has gone.
Easily the most insidious drag on the aspiring player's progress is the
early forming of negative study habits - all the Masters agree on this - and
of these the 'trial and error' habit is the worst. As Nathan Rubin puts it,
'Hindsight is a poor substitute for foresight.' This, of course, is very true,
and the quality of foresight can only be exercised when you have a firm grip
on the present. You will gain this mastery by learning correctly to analyse.
Start now.
C H A P T E R F I V E
Not a stroke of genius
It is convenient for study purposes to divide the game into three phases;
opening, mid-game, end-game. This division is not entirely artificial as the
chief motives underlying each phase are really very distinctive. The
dominant theme of the opening may be said to be preparation for the battle
which rages throughout the mid-game; the conflict of the mid-game is
resolved in the end-game. In this latter we seek to prove the real value of
the seeming advantages gained or lost during the earlier play.
One need only define the purpose of the end-game to see that this must be
the most vital phase of the game. The preceding phases are concerned with
creating good prospects, in the end-game we consider the actual result, win,
lose, or draw. A slip at this stage and all the brilliant ideas of the past
become worthless. On the other hand it is the end-game, demanding as it does
both precision and artistry, that may give one the chance to recover from a
weak position and turn defeat into victory. In draughts the best player wins
and the proof is here - in the end-game.
Let us now analyse some illustrative positions.
DIAGRAM 34
Study by Cudney
White - to play
+------------------------+
|::: ::: ::: ::: w |
| w ::: ::: ::: :::|
|::: ::: ::: b ::: |
| ::: ::: ::: :::|
|::: w ::: B ::: ::: |
| ::: ::: ::: :::|
|::: b ::: ::: ::: |
| ::: ::: ::: :::|
+------------------------+
Black
As always, we should begin with a general survey in terms of space, force,
and time, in order to get the feel of the situation. We see here that Black
occupies the centre, possesses a king and has a time-count of 16 to White's
8, but does not have 'the move'. By the way, you should in all cases make
these counts for yourself - don't just wait for me to tell you - constant
practice in this will soon enable you to sum up matters very quickly so that
you can then get on to the business of forming a plan of campaign.
In this position a marked feature is that White is very backward in
development. His total of a mere 8, with 3 men on the board, is an average
development of only 2.66.
The disadvantage of this in an end-game is that undeveloped men are in
danger of being held by opposing pieces and prevented from moving while at
the same time the opponent crowns several kings. Here, White has two such
men; if Black is able to fix these and obtain for himself three kings, then
an easy win for Black will be in sight. White will have made only one king
which would be unable to hold out for long against an attack. White needs at
least a couple of kings to make any sort of stand.
If White's urgent need is to develop his men then Black must try to hinder
those efforts, and must also utilize his own superior development to
strengthen his grip on the centre.
Such considerations will lead both players through Diagram 35 to Diagram
36:
DIAGRAM 35
White - to play
+------------------------+
|::: ::: ::: ::: w |
| ::: ::: ::: :::|
|::: ::: b ::: b ::: |
| ::: ::: ::: :::|
|::: w ::: B ::: ::: |
| w ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
+------------------------+
Black
We pause at Diagram 35 - to observe that White must continue with his
scheme, yet you may wonder why White does not here take the opportunity to
exchange off Black's king and so hasten the development. The answer is that
after this exchange Black would soon make up his advantage again to 7 moves,
by getting two kings; and in addition 'the move' would then be against White
- so Black would be stronger than before. In fact, the White king would have
to scurry across to the double corner to avoid instant loss and then Black
would win as shown in Chapter Four, at Diagram 29.
You will notice that in the series of moves leading from Diagram 35 to 36
White has other chances to allow an exchange, but always to Black's profit.
This demonstrates the power of the Black king at the centre in being thus
immune. It also gives a clue to the lines along which Black will build his
attack.
We will now review the situation:
DIAGRAM 36
Study by Sweeney
White
+------------------------+
|::: ::: ::: ::: w |
| ::: ::: ::: :::|
|::: ::: B ::: b ::: |
| ::: ::: ::: :::|
|::: ::: B ::: ::: |
| ::: ::: ::: :::|
|::: W ::: w ::: ::: |
| ::: ::: ::: :::|
+------------------------+
Black - to play
Black has made much progress in the space element and is still well ahead
in development. On the other hand, White will soon equalize in force, and as
you will see when the opposing Kings clash, White has the advantage of 'the
move'. White clearly has relieved the situation of its immediate perils - yet
we saw that White feared an exchange. Black may make something of this.
We will now wish really to get down to the crux of this position and
examine it move by move, as we always must when a situation presents
conflicting issues. For that reason it will be convenient to evolve some
form of notation, whereby we shall be able to refer to a particular move by
name, as it were.
This is very easily done when we recall that every move is made in a
diagonal direction. By indicating the diagonal along which the move is made
- and the rank to which the piece is moved - in a letter and a digit the
precise move is named. This G5 indicates that a piece is moved along the
G-line to the fifth rank. Naturally, if it is Black's move then it is made
to Black's G5; so with White. The Diagrams, 13 and 14, will already have
clarified this point; I simply refresh your memory.
Using this notation has the vital and practical consequence of intensifying
your grasp of the various diagonals and squares EVERY TIME YOU MAKE A MOVE,
THUS AUTOMATICALLY IMPROVING YOUR SKILL. No other system of notation could
possibly do that.
Returning to Diagram 36: if the Black player is to make any headway then
he must complete his development by getting a third king; yet at the same
time he must not allow the White man at D1 to escape, as this grip is
virtually the only significant advantage he has. This is going to be a
fairly complex manoeuvre and in such cases it is best where possible to
utilize the general superiority in position, and proceed by threats. In this
way we adopt a policy of constraining the enemy plans whilst carrying out
our own.
Black begins with the move G5, a direct threat to exchange kings; White
must move his king out of range and plays E8 in order to keep two active
pieces together for mutual protection - if Black can split these two then
both would be weakened. Black now plays A3 which forces the reply F8; and
now G6 poses an indirect threat.
DIAGRAM 37
White - to play
+------------------------+
|::: ::: ::: ::: w |
| ::: ::: ::: :::|
|::: ::: B ::: b ::: |
| ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: B ::: :::|
|::: ::: ::: ::: |
| ::: W ::: W ::: :::|
+------------------------+
Black
As I have just referred to 'direct' and 'indirect' threats I may as well
explain the distinction I see in these terms. A direct threat is one that
you intend to execute on your next move, and would in fact carry out if it
were your turn to move now - he is in the line of fire and the onus is upon
him to step out of range. An indirect threat is one which is implied: if he
plays this and that you will play here and there - he is not now in the line
of fire, but one false step and you will let him have it. In a general way,
one might say that direct threats are most effective when one is ahead in
development, indirect threats when one is superior in space. Here, Black
has the pull both ways and is able to use both types of threat.
Well now, let us see what is this indirect threat which Black sets. It is,
again, the threat of exchange, which haunts White throughout this end-game.
If White were now to play F7, then there is a neat cut by Black via C7, C5,
D7, D3, E3, and a loss for White.
It is characteristic of an indirect threat that often one is able to hold
it over the opponent's head for a considerable period, in this way confining
his moves. From Diagram 37, White is compelled to play E7, and after C7, E8,
C8, the threat is still 'on', and the way is now clear for Black to get his
third king and return with it to F6. Each time the White king plays back to
E8 in an attempt to release his fellow king the indirect threat of the
exchange prevents this from coming about. Eventually Diagram 38 is formed.
DIAGRAM 38
Study by Wardell
White
+------------------------+
|::: ::: ::: B ::: w |
| ::: ::: ::: :::|
|::: ::: ::: B ::: |
| ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: B ::: :::|
|::: W ::: ::: ::: |
| ::: ::: W ::: :::|
+------------------------+
Black - to play
Black now completely dominates the scene and so it is up to him to
conceive a comprehensive plan to embrace the remaining action. Attack upon
the White kings seems indicated, yet unless the purpose of the attack be
defined it cannot be properly executed. There is no point in attacking the
kings in order to make the man come forward: the defending kings do not stand
in the path of the man and so they would not be hampered by it's approach.
Can either be driven into its path? Perhaps, if the White kings can be
split, but by what threat?
Here we have it again, the threat to exchange. The broad plan now begins
to take shape in your mind. You already hold one White king helpless; a
threat to exchange off this king would compel the other White king to seek
safety elsewhere, as it could not remain in the single corner area, alone.
Le us see this in operation. Black plays E7; then follow E8, E6, E7, F5, and
White dare not go back E8 once more for then Black will get the exchange
with F4, F7, F5, etc. White must therefore play D6, so as to counter F4 with
F5 with intent to flee to the opposite double corner. This successfully
forestalls the exchange but, unfortunately for White, allows Black to move
now A4. Black thus has separated the White Kings. See Diagram 39:
DIAGRAM 39 DIAGRAM 40
White - to play White
+------------------------+ +------------------------+
|::: ::: ::: ::: w | |::: ::: ::: ::: w |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: B | |::: ::: ::: ::: B |
| ::: ::: ::: :::| | W ::: B ::: ::: :::|
|::: W ::: B ::: ::: B | |::: ::: ::: ::: B |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: W ::: ::: |
| ::: ::: W ::: :::| | ::: ::: ::: :::|
+------------------------+ +------------------------+
Black Black - to play
White may now meekly submit to Black's plan by playing B7 and into the
double corner, or make a desperate effort to re-unite his kings - by F4,
compelling Black to A5 whereupon White plays F7 - forming Diagram 40. Clearly
White intends to run this king to E6 and so release his king at F4. It
begins to look as if White has cleverly drawn Black's attack to one side
of the board so as escape via the other. Is Black too far away to do
anything about it, or can Black yet persuade White into the end-game of
Diagram 29 as he been trying to do all along?
I think it will be best if I leave you to work out the correct result for
yourself, as you will be able to do if you have grasped the basic themes that
we have discussed here.
When you are satisfied that you have correctly analysed this situation, we
can proceed to other matters.
I will now show you a couple of end-games from my own play. These will
not only illustrate further important principles but will also give you some
idea of the considerations which pass through a player's mind during a game.
DIAGRAM 41
Match 1955
Black (Cohen) to play
+------------------------+
|::: ::: ::: ::: b |
| ::: ::: w ::: :::|
|::: ::: ::: ::: b |
| ::: ::: W ::: :::|
|::: ::: ::: ::: w |
| ::: ::: ::: :::|
|::: w ::: ::: B ::: |
| ::: ::: B ::: :::|
+------------------------+
White (Oldbury)
The dominant features here of course are the White strength in the centre
and the Black weakness in the single corner. It is not hard to see that
White has in view an attack on the two Black kings with three White kings,
eventually to compel the move D2, then an attack on what will then be
an exposed man and a win. All this, by now, should be routine stuff to you.
What is not so easy to see is how Black could avoid this, yet the proper
defence may be found if we apply principles which have already been stated.
We find that in this type of end-game the defending player should endeavour
to take his kings to that side of the board furthest from any undeveloped
men. In this way freedom of action is kept.
This defensive theme is put into operation in the following sequence: G6,
F8, F7, F7, C8, C3, E7, C4, D6, B5, G5, and Black is quite safe.
In the actual game, my opponent did not adopt this defence but let his
kings remain in the double corner zone. This allowed me to build up my
attack in the approved manner and eventually force the advance of the man on
D1.
From Diagram 41, Black moved B6; after which came F8, F7, B7, C6, C3, C5,
G(7)6, C6, and I then had a clear run for the third king needed to reinforce
the attack, the climax of which came at the point shown in Diagram 42.
If you will examine this closely, you will observe that if Black continues
moving his kings then White soon brings about an exchange, to an easy win.
In the game, this meant that the long-awaited D2 had then to come for me. The
rest was straightforward:
DIAGRAM 42
Black - to play
+------------------------+
|::: ::: ::: ::: b |
| ::: ::: ::: :::|
|::: ::: ::: ::: b |
| ::: W ::: W ::: :::|
|::: ::: ::: ::: w |
| ::: W ::: B ::: B :::|
|::: ::: ::: ::: |
| ::: ::: ::: :::|
+------------------------+
White
B4, C7, C6, A7, C(4)5, F8, A6, F7, B7, F8, B8, F7, F7, winning the exposed
man and the game.
My next example is very different.
DIAGRAM 43
Match 1955
Black (Oldbury)
+------------------------+
|::: ::: ::: ::: |
| ::: ::: ::: w :::|
|::: ::: ::: w ::: b |
| b ::: w ::: ::: :::|
|::: w ::: ::: ::: b |
| ::: w ::: ::: :::|
|::: ::: B ::: ::: |
| ::: ::: ::: :::|
+------------------------+
White (Cohen) to play
The first thing to be noted is an unequal number of pieces. This came
about because on approaching the end-game I sacrificed a man so as to gain
position. The soundness of such play will always depend on the extent to
which gains are made in other elements. You give up material so as to gain
space or time or both space and time. If your sacrifice in force does not
make these compensating gains then it cannot be sound, no matter how
brilliant it may seem. For this reason it is most important when considering
sacrificial play to attend with care to these matters, by making a proper
valuation of the position.
These comments may tend to disillusion those who are under the impression
that when a player gives up a piece to advantage he does so as a result of
inspiration, a stroke of genius as it were. In my own play I am known to
employ very frequently the sacrifice in force, and I am able to do this
simply because I have developed an understanding of the principle involved.
Any intelligent player can do the same.
We will now find out whether Black has in fact gained compensation. A
time-count shows Black at 20, but White at 25.
It would seem Black lags in development, until it is realized we are not
taking into account the fact that Black has only 4 pieces against White's 5.
When the opposing forces are unequal in number then we must take average
development for a proper comparison. Thus, Black is 20 divided by 4 = 5;
White is 25 divided by 5 = 5: they are level in development.
Some people say you can prove anything with figures, so I must hasten to
assure you that what I have just shown is not mathematical hocus-pocus. It
is simply that when the forces are equal in number, one does not usually
speak of 'average' development, for as a rule there is no need: the main
concern being to find out which side is ahead, in those cases the total count
will tell us this without troubling to work out averages - but here the
forces are unequal in number and only the 'average time-count' will reveal
the true state of affairs.
In space. the dominant feature is the grip which Black has on the two
White men on the B diagonal. (It is appreciated by now, I trust, that when I
refer to White pieces I refer to diagonals as seen by White, and so with
Black. The advantages of independent notation are well understood by those
who play chess and are in even greater evidence in draughts.) If Black can
mantain his grip on these men then he virtually equalises the situation. as
White can bring into action no more than 3 kings and Black will do the same.
This hold constitutes an advantage in space, and is the only pull Black has.
Yet again the simple action of summing up the integral parts of a position
suggests to us the probable course of the play. White will try to use his
advantage in force to break Black's hold. Though both sides can obtain 3
kings, the Black king at C7 is tied down to the job of seeing that the White
men do not break away. Black then has only 2 free kings; if the 3 White
kings can deal effectively with these then Black will have no choice but to
move his king from C7 and so release the men.
This sounds a promising line of attack and it would probably win the game,
except that the White kings will not themselves be entirely free to roam at
will. This is brought home when we observe Black's threat to play C8 and
regain his lost material straightaway. While it is easy to remove any
immediate danger, by moving A6, yet the threat is still in the air and it's
presence is enough to dilute the potency of the White attack.
From Diagram 43, the initial moves simply carried out the desire of each
player to develop his position; thus after A6, we continued B6, F7, B7,
F8, B8, E8, C4, F7, B5, F6, B6, B7, A7, D5, A8, G8, G7, E7, G6, G6, forming
Diagram 44:
DIAGRAM 44
Black - to play
+------------------------+
|::: W ::: ::: ::: |
| ::: ::: ::: W :::|
|::: ::: W ::: ::: |
| b ::: ::: ::: :::|
|::: w ::: ::: ::: |
| ::: w ::: B ::: :::|
|::: ::: B ::: ::: |
| ::: ::: B ::: :::|
+------------------------+
White
At this stage, Black has an average time-count of 7 against White of 6.2,
so in this respect he had made a little progress and has also brought 3
kings to bear on the weak White men. Yet he has no chance to play C8 with
effect, and an indirect threat (if C5, White will reply C(4)5!) somewhat
limits his field of action. Meanwhile, White prepares a far-sighted attack
which will entail playing his king on E7 to F4, then bringing the king at G8
around the board to F5 and threatening to exchange kings.
These considerations influenced the moves which followed, thus: B7, E6, B6
(played to intercept the White king's advance by meeting E5 with B5), and so
on, eventually getting the position shown at Diagram 45:
DIAGRAM 45
Black - to play
+------------------------+
|::: ::: ::: ::: |
| ::: ::: ::: :::|
|::: ::: W ::: ::: W |
| b ::: ::: ::: W :::|
|::: w ::: ::: ::: |
| ::: w ::: B ::: B :::|
|::: ::: B ::: ::: |
| ::: ::: ::: :::|
+------------------------+
White
As you saw, White could not get a king to F4 earlier and so the attack had
to be built up in a slightly modified form. At this point Black faced
several indirect threats, including the formidable one that if now A5, then
the beautiful D4 winning sacrifice.
The game continued B7, E4, C4, E4, G6, E5, and now Black was able to shift
the grip by C8, F6, and C(6)7, securing the draw. The soundness of the Black
defence was thus established: however, my opponent is to be complimented on
playing for every winning chance.
A large proportion of these end-games in which one side is a man down
revolve around a theme similar to that just demonstrated. The defending
kings hold down a man, perhaps at the edge of the board, and opposing kings
try to set it free. If the man can be held indefinitely then the game
results in a draw; if the attackers can get the man away then they win.
The method of attack takes the form of threats to one of the defending
kings, in an attempt either to tie it down or get an exchange. If these
attacks succeed then the other defending king(s) will have to move, thus
releasing the man. You will see that this principle of attacking a king so
as to force other pieces to move is a fundamental concept of end-game play
and cannot be over-emphasized.
To complete this chapter on end-game strategy I will leave you with a
study which incorporates in one way or another most of the points I have
brought out. It will serve as an exercise by which you may improve your
technique.
DIAGRAM 46
Study by Oldbury
White
+------------------------+
|::: ::: ::: ::: |
| w ::: ::: ::: :::|
|::: ::: ::: ::: |
| ::: ::: w ::: :::|
|::: B ::: ::: ::: B |
| ::: ::: ::: :::|
|::: ::: ::: ::: W |
| ::: ::: ::: :::|
+------------------------+
Black to play - what result?
C H A P T E R S I X
Don't run out of moves
Study of the mid-game is the study of formations. You must study the
mid-game before the opening. You make moves in the opening so as to bring
about a position which will favour you, either because it is strong in
theory or because you well understand how to handle that particular set-up.
If you know nothing of the mid-game then how are you to do this?
When we use a formational pattern we are playing in the element of space.
The amount of space we control will depend on the size of the structure; the
larger it is the more squares we shall control. The 'character' of the
formation, attacking or defending, will be decided by the exact location of
the squares we occupy when we make our formation.
Very well, you say, from this day we will build bigger and better format-
ions. What do we do with them, once built?
The answer to that is, you do little with the actual formation; when you
have set it up you make waiting or developing moves with your other men. Your
formation will have given you the superiority in space and your opponent
will be forced on to inferior squares as long as you keep control. If your
formation is reinforced to withstand attempts to break it down, and if also
you have in hand enough waiting moves to counter your opponent's, he will be
forced into a weak position. In effect, you will have run him out of moves.
Now in a very general way, that is the major underlying motive of mid-game
play. Either you are trying to create such a pattern to your advantage or
you are aiming to frustrate your opponent's efforts along those lines. In
still other cases, both sides seek to prevent such a pattern from being
formed and so it never actually appears, yet it is implied in the play.
The most effective formations will comprise an oblique chain of men, each
preserving some degree of mobility. In proportion as such a chain of men can
occupy or overlook an important diagonal of the board so will it be enhanced
in power.
It stands to reason that, having built up a formation, the more reserve
men we still have in action the more waiting moves shall we be able to
produce, without disturbing our formation, and the better our chances of
embarrassing the enemy. At the same time, the state of our development will
also affect our supply of waiting moves.
We will now analyse some situations from the mid-game. In Chapter One I
suggested that occupying the A-line characterizes attack, so let's begin at
that point (see Diagram 47).
DIAGRAM 47
Study by Oldbury
Black - to play
+------------------------+
|::: b ::: b ::: b ::: b |
| b ::: ::: b ::: :::|
|::: b ::: ::: ::: b |
| b ::: w ::: ::: b :::|
|::: ::: w ::: ::: b |
| w ::: ::: w ::: w :::|
|::: ::: w ::: w ::: w |
| w ::: w ::: ::: w :::|
+------------------------+
White
White has an ideal formation; comprising 5 men on the A-line with
supporting units in the single corner zone and 2 ready for attack along the
G-line. Black, too, has 11 men but in contrast to the Whites they are all
placed around the edges of the board, in what seems to be no particular
formation. The highest number of men Black has on any one diagonal is 4, and
these on the weak B-line. That White is superior in space is not to be
disputed.
In the element of time we find that Black has a count of 27, and that
White's too is 27. This suggests equality, yet in theory there is never
absolute equality in development - certainly not in the opening and mid-game.
I shall demonstrate this point, as it is of importance.
In Chapter Three, you may recall, I stated that to be ahead in development
early in the game is to be thought a disadvantage in time, and I gave my
reasons. These amounted to the idea that here there is a possibility of being
run out of moves - either out of good moves or out of any moves at all. In
theory, this means that the player who will first feel the pinch will be he
who has the higher time-count, or, when the counts are level, he whose turn
it is to move.
In the normal course of events the only action which can alter the
relative development of the two armies is the action of jumping. Thus, on
the basis of the time-count, one can legitimately declare that if no further
jumps are made in a particular game then it is possible to forecast which of
the two players will ultimately find that 'the move' is against him.
At the position we are now examining it is Black to play, so that despite
a level time-count Black is at a disadvantage in development. Unless Black
somehow can bring about an exchange or an opportune sacrifice, then he cannot
look to the future with relish.
I now show you a simple way to test the conclusions reached from the
time-count. Make these moves, BUT WITH THE WHITE MEN ONLY: B3, D2, C4, G4,
G3, G2, C3, C2, eight moves in all. NOW MOVE THE BLACK MEN: D2, A2, A3, D3,
F2, C2, six moves in all. We see that White has in hand two moves more than
Black. Now if you will reset the men as in Diagram 47 you can play through
these two sequences of moves as they would occur in an actual game, altern-
ately Black then White. Thus you will see it in action. We get, starting with
Black: D2, B3, A2, D2, A3, C4, D3, G4, F2, G3, C2, G2 and White wins, with
two moves to spare.
You must never forget that this theory concerning development of the open-
ing and mid-game carries the clause, 'if no more jumps'. You cannot justly
expect an automatic win because the count is in your favour. In many cases
your opponent, if he is cute enough, will conjure up some alteration in the
state of things which will ease matters for him. Yet the mere fact that the
onus is upon him to do something about it must surely be deemed a concrete
advantage to you.
From our survey to date, one is tempted to regard Black's cause as a lost
one, and when in addition I tell you that this position has been published
many times and is pronounced a White win by all the critics after extensive
'analysis', you may wonder what there can possibly be said in Black's
defence.
Let us see. We would be doing less than justice to the depth of the
situation if we were to dismiss it so lightly. After all, so far we have
barely more than glanced at it; and whether the position has ever been
analysed in our sense of the term is to be very much doubted.
If White's strength in space is in his A-line, on which he has a chain of
5 men, then his weakness, if any, may perhaps lie in the B-line, on which he
has but one man. Black has a supported man at F4 and maybe there are counter
chances in that direction at some future date. These chances would be
improved by playing a man to A3, forcing an exchange and thus preparing the
move F5.
A defensive scheme begins to emerge; it remains to discern the moves that
will fit into that scheme. Black has only one move which answers the various
requirements, and that is F2. This move discourages White from playing B3 by
an indirect threat: if B3, then Black will reply C5, exchanging several men
and breaking up the attack. Black also prepares to follow up the idea of
playing A3 if any further danger of a closed position should arise.
It will now be up to White to find waiting moves, so that after the
exchange coming from Black's A3 move White will be able to play C3 and so
replace the man removed in the exchange. If White does not do this then
Black will get in his ultimate idea of F5.
These weighty considerations on both sides lead to the following play.
From Diagram 47, move F2, D2, D2 (delaying his A3 move so as to give White a
chance to play D3 first), G4 (holding back D3 as he wants to play C3 a few
moves later), A3 (cannot delay any longer as White now threatens to play B3),
G3, E5, C5, A2 (come again), C3, A3, and we are at the climax of the
mid-game.
DIAGRAM 48
Black
+------------------------+
|::: ::: ::: b ::: |
| b ::: ::: b ::: b :::|
|::: b ::: b ::: ::: b |
| b ::: w ::: ::: b :::|
|::: ::: w ::: w ::: b |
| w ::: ::: w ::: w :::|
|::: ::: w ::: w ::: |
| ::: w ::: ::: w :::|
+------------------------+
White - to play
White is now at the critical juncture where he must commit himself to a
positive line of attack. If we summarize what has gone before, White has
tried to capitalize on his advantage in time by playing a waiting game, to
create a closed position wherein Black could be run out of moves. By forcing
some exchanges Black has avoided this danger, thus neutralizing White's pull
in the time element. As the number of men on a board is reduced so the
significance of development under goes a change. We now approach the turning
point at which to be ahead is something to be sought after and not to be
shunned.
White has retained considerable superiority in space; but now it is
desirable to speed up his development, which can be done by continuing D5,
E5, C5, G5, A5, C6, A4, B7, A3.
If you will here make a time-count you will discover Black's to be 14 and
White's 20; thus has White gained 6 moves in development on these exchanges
of material. As in addition White controls the centre squares he can feel
assured of entering the end-game with good prospects.
This chapter is concerned primarily with the mid-game, therefore I shall
not discuss in detail any of the end-games which evolve from the examples of
mid-game play given here. Any lengthy discussion would be out of place and
would tend to obscure the principles of mid-game analysis I am trying to
establish. I think it will be enough if I simply give what I consider to be
the best continuation for both sides, which will give you a general if not
specific guide to the way the ending in question should properly be played.
You can always make a deeper analysis for yourself if you feel so inclined,
and at that it will be good practice for you so to do.
In the position above: after the exchanges Black make a good escape by C4,
C6, E4, A6, G4, A4, G6, E6, F5, E2, E6, E3, E7, E4, E8, E5, D3(the saving
touch, as C7 would loose), D7, C7, D8, C6, D7, C5, D6, A6 - Drawn.
Before leaving this study, I would like to refer again to Diagram 48. At
that stage it appeared that White could have kept his A-line control by
playing another waiting move, G2. Why did he not do this?
In principle, this type of move is inferior, yet it is very often played
and even by players of experience. The chain of men along the A-line 'rests'
upon the man at A1 - and to remove the base of the formation in this tends
to weaken the whole line and is not a thing that one should do from choice.
After this move, it usually takes the opponent very little time to break
down the formation, thus taking the initiative. Here, for instance, after
G2, E5, C5, Black gets in with his F5 move, forcing the reply G5, and then
C5 takes all the wind out of White's sails.
This last move is characteristic and I give another illustration of the
point:
DIAGRAM 49
Match, 1955
White (Oldbury)
+------------------------+
|::: w ::: ::: w ::: |
| w ::: w ::: w ::: :::|
|::: ::: ::: ::: w |
| ::: b ::: ::: w :::|
|::: ::: b ::: ::: w |
| ::: ::: b ::: b :::|
|::: b ::: b ::: b ::: |
| ::: ::: ::: b :::|
+------------------------+
Black (Marshall) to play
The very best move here was C3, but my opponent played G2. This gave me
the chance to initiate a counter-attack, thus A3, C3, E5, C5, A2, D5, C2,
B3, C5(decisive), E5, C5, B4, C6 and White soon won.
Though an early A-line formation is a powerful offensive weapon, it may
perhaps be said to reveal too clearly the player's intentions. Once you
have embarked upon this type of attack you have committed yourself to a line
of action from which it is rather difficult to depart. This does not in the
least detract from the actual strength of the A-line formation, but it does
mean that your opponent is able to concentrate on a specific line of defence.
(As they say in boxing, you 'telegraph' your punches.)
For these reasons it is expedient now and again to vary the processes of
formational play. Instead of setting up the formation and then maintaining
it by employing waiting tactics, the player first makes a series of non-
committal moves, creating a fluid situation from which will emerge the
chosen formation at a later stage. Such a method of play will prove subtle,
indeed, and the opponent may have much difficulty in anticipating the exact
intentions behind the quiet manoeuvres.
DIAGRAM 50 DIAGRAM 51
Scottish Championship, 1950
White (Scott) White - to play
+------------------------+ +------------------------+
|::: w ::: w ::: w ::: | |::: ::: w ::: ::: |
| w ::: ::: ::: w :::| | w ::: w ::: w ::: :::|
|::: ::: ::: ::: w | |::: ::: ::: w ::: |
| ::: b ::: w ::: w :::| | b ::: b ::: ::: :::|
|::: ::: ::: ::: | |::: ::: b ::: ::: w |
| ::: b ::: b ::: :::| | ::: ::: b ::: :::|
|::: ::: b ::: ::: | |::: ::: ::: ::: |
| b ::: b ::: b ::: b :::| | ::: ::: b ::: b :::|
+------------------------+ +------------------------+
Black (Oldbury) to play Black
From Diagram 50 Black proceeds with discretion, giving little sign of a
coming attack: D2, D3, C3, B5, C4, E2, B5, A5, E5, C5, D4(moving into
position), A2 (White does not continue his activities on the opposite wing
and the pause is fatal), and now Black strikes with E3, C7, E3 - see Diagram
51.
With a superiority in space by virtue of the A-line control, and an
advantage in time of 4 moves, Black's game now has a powerful look. Add to
this the direct threat to break through for a king and the indirect threat
that if White now plays D4 then D6, B4, and F2 quickly ends all resistance,
and clearly Black should win. From Diagram 51 the game concluded A3, A6, G4,
A6, D4, B7, F4, B7, D5, A5, E5, B8, B3, F7, B4, F6, F6, F2, F7, F3, B7, F4,
B8, A2 - Black won.
Another example of this 'slow-motion' theme:
DIAGRAM 52 DIAGRAM 53
British Championship, 1954
Black (Scott) Black
+------------------------+ +------------------------+
|::: b ::: b ::: b ::: b | |::: b ::: b ::: b ::: |
| b ::: ::: ::: b :::| | b ::: ::: ::: b :::|
|::: b ::: ::: ::: b | |::: b ::: ::: b ::: b |
| ::: ::: b ::: :::| | ::: ::: b ::: :::|
|::: w ::: ::: ::: | |::: w ::: ::: ::: |
| w ::: ::: ::: w :::| | w ::: w ::: ::: w :::|
|::: ::: ::: w ::: w | |::: ::: ::: w ::: w |
| w ::: w ::: w ::: w :::| | ::: w ::: w ::: w :::|
+------------------------+ +------------------------+
White (Oldbury) to play White - to play
At Diagram 52, White seems far removed from any thought of attack. Yet by
encouraging Black to waste but a single move in an idle threat White gains
enough time to take control of the centre with an A-line formation. The play
went D2, D3, D3. At that point Black could have anticipated White's scheme,
by now moving E2. which would have enabled Black to follow up with E3 and
then G4 before White could get into position. Instead of that Black chose D2
and a direct threat. See Diagram 53.
I was now ready to show my hand. The game continued G4, A6, G4, E2, D4, A2,
C5, B4, A3, A3, A2, E5, C5, B5, G5, B3, G6, B4, C7(neat climax), B3, E2, F4,
B3 - White won.
We will now see something quite different - attack along the D-line.
Forming a chain of men from D1 to D5 will generally prove an ineffective
method, in contrast to A-line formations, and for several reasons. To begin
with, as the D-line is the main dividing line between the opposing armies a
chain of men built along the D-line will point in a neutral direction, as it
were, and not at the heart of the enemy position. Then, if we examine such a
chain we observe that the men at D1 and D2, the base, are virtually out of
play and have no other value. This is in contrast to men at A1 and A2, which
can not only act as supports to a chain but can also confine enemy units
which may stand at their A7 and B5.
The merit of the D-line attack is in the establishing of a single advanced
post rather than the erection of an unwieldy structure. For instance, a man
at D5 prevents the enemy from building along his A-line; better still at D6,
where it cramps an opponent's undeveloped single corner with indirect
threats to get through to the king-row. Such advanced posts generally need
only light support, thus your other men are not kept inactive. On the other
hand, if through an injudicious advance a man comes to need much protection
from its fellows, without itself contributing to the strength of the
position, then it has become a liability and the player will regret not
having surveyed the lie of the land with more care.
Let us now see some of these pros and cons in action. Firstly, Diagram 54:
DIAGRAM 54 DIAGRAM 55
British Championship, 1954
Black (Marshall) Black
+------------------------+ +------------------------+
|::: b ::: b ::: ::: b | |::: b ::: b ::: ::: |
| b ::: b ::: b ::: b :::| | b ::: ::: ::: :::|
|::: ::: ::: b ::: | |::: ::: b ::: b ::: |
| b ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: w ::: b ::: w | |::: ::: w ::: b ::: w |
| w ::: w ::: ::: :::| | ::: ::: ::: :::|
|::: w ::: w ::: ::: | |::: ::: ::: ::: |
| w ::: w ::: w ::: w :::| | w ::: w ::: w ::: w :::|
+------------------------+ +------------------------+
White (Oldbury) to play White - to play
Not as in an A-line set-up, here White seizes any chance to get an attack
going, thus D5, D5, D5 was played without delay, with D6 in view at my next
move. Black met this threat by B3, B3, D5, D5, D3, D7, D3, C4, F6, D4, A3,
forming Diagram 55.
It would seem that all the activity along the D-line has fizzled out, yet
we are now at the climax. Observe two features: that White has an unbroken
first rank; that the Black man at D3 is trying to stem the advance of two
White men at one and the same time. Add a tiny flash of imaginative insight
and the course of action is clear. White will make a sacrifice and then run
through for a king, leaving Black with an end-game headache.
This I did, and the ensuing play ran: D5, D5, F5, B2, E6, B3, E7, B4, E8,
E4, C7, G3, F6, B5, D2, G2, B2, F4, D5, G6, G3, B7, E4, B8, D3, E5, D4, F6,
A5, F5, E5, E6, E6, D7, C6, D8, G7, D7, B8, D6, B7, D5, G6, G6, C5, B7, C4,
B6, E7, G5, E8, A5, C7, A4, A2, A5, F6, G3 - Drawn. A very hard fought
contest.
In the following example, the opportunity for immediate attack is not
present and both sides must proceed with care in an involved situation (see
Diagram 56).
DIAGRAM 56
British Championship, 1954
White (Cohen)
+------------------------+
|::: w ::: w ::: w ::: w |
| w ::: w ::: w ::: :::|
|::: ::: ::: ::: w |
| w ::: ::: b ::: :::|
|::: ::: ::: ::: w |
| b ::: b ::: b ::: :::|
|::: ::: ::: b ::: b |
| b ::: b ::: b ::: b :::|
+------------------------+
Black (Oldbury) to play
Assessing the bare facts: there is equality in force, each side has a
time-count of 22, and Black occupies the centre.
You will see that both Black and White enjoy a very high degree of scope
and free action and from this it is fair to deduce that any 'pull' that may
exist in such a position will be of a slight nature. We must also note that
it would be plain silly to make an 'analysis' of the 'trial and error' sort,
as it is not possible to visualize even what the next FEW moves will be, let
alone the general course of events. In fluid situations like these, the
'expert' begins to flounder helplessly, seeking a move but lacking the grasp
of basic principles so vital to a comprehension of what is required.
Conversely, it is here that the Master player is able to demonstrate his
skill by evolving an intelligent plan despite a maze of possibilities.
It is self-evident, I think, that where a positional advantage is slight,
then may it so much more easily slip away from us. We must make of it what
we can, while we can. Only awareness of detail will tell us how we may do
this.
We have already seen that Black occupies the centre of the board and, to
be more specific, with a man at the fifth rank. We must determine the effect
that this man will have on the play. You will note that the man is on the
two diagonals, D and G. On the D-line Black 3 men to White's 1 and on the
G-line (White's A-line) there are 3 Black men and 2 White. Thus, Black has a
majority in strength over White on both diagonals. This suggests that a man
on the square which intersects the two may be of some import.
It may also suggest to Black a course of action, namely, that of building
up a formation along the D and G diagonals - in the shape of a spearhead, to
be driven in the enemy ranks by the move D6 or G6. Seeing that Black
controls the centre one may quite reasonably take the view that White can do
very little to thwart this scheme.
Yet if the Black player were to embark without more thought than this upon
such a line of play, he would probably lose. This is because the time-count
has not been included in the calculations. In the congested situation that
such play would almost certainly lead into, the time advantage would favour
White, because at present it is Black to play. White would need only to
place supported men at B3 and E3, gripping the Black formation, then play a
waiting game, until Black is bound to commit himself to a bad move. Thus we
see an entirely different conception on the part of White; the pincer move-
ment. White will attempt to crush Black in the centre.
This does not mean that Black must throw aside the thought of a spearhead
attack - but it must be modified in such a way as to preserve a degree of
mobility. Black must forestall White's efforts to establish a stranglehold.
DIAGRAM 57 DIAGRAM 58
White - to play White
+------------------------+ +------------------------+
|::: ::: w ::: ::: | |::: ::: w ::: ::: |
| w ::: w ::: w ::: w :::| | ::: w ::: w ::: w :::|
|::: w ::: w ::: ::: w | |::: ::: w ::: ::: w |
| w ::: ::: b ::: :::| | w ::: w ::: b ::: :::|
|::: ::: b ::: b ::: w | |::: ::: ::: b ::: w |
| b ::: ::: b ::: :::| | b ::: ::: b ::: :::|
|::: b ::: b ::: b ::: b | |::: b ::: b ::: b ::: b |
| ::: ::: b ::: :::| | ::: ::: b ::: :::|
+------------------------+ +------------------------+
Black Black - to play
Fron Diagram 56, the actual moves played carried out these ideas on both
sides, as follows: E4, (increasing the Black majority on the G-line, and
stopping White from moving E3 because then Black would get in D6 straight-
away!), D2 (also an indirect threat: if Black moves D4 then White will start
a pincer movement by B3), D2, G3 (still waiting for D4), E2, E3 (trying
another way; intending to follow up with E2 and then the binding B3), D4,
E2, A3 (just in time), G2 (frustration: White cannot get in his B3 move, for
Black will reply E5 and win), A2, reaching Diagram 57.
Black has prevented White from getting a grip and White must now be
content to seek what chances he may in the end-game, by bringing about some
exchanges. White dare not play E4, as this would free Black in the centre
and allow him to complete his build-up via D3, E3, F3, B7, F3 (the desired
pattern), B2, D6 (a terrible blow), B4, F4, D3, G3, and a Black win.
In the game, White played G4, A6, G4, forming Diagram 58. With this
exchange, the dangers of the mid-game pass and the players approach the
end-game.
From here the moves were: B3, G5, A5, F7, B3, B3, D4, B4, A3, B2 (if B6,
D3, B7, then Black 'spears' White by G3 - the threat lingers on), D3, B3,
C4, B6, C5, B7, A6, B8, B8, F7, G3, F5, F4, F6, B7 - Drawn. Perhaps a model
game on this type of structure.
It seems rather incongruous to refer to a spearhead in defence, yet at the
very beginning of a game each side possesses a formation of this shape which
has great defensive value. This is the group of men which is on the squares
E1, E2, E3, F1, F2, and G1. (The 'triangle theory' of Pierre Mallet, 1668.)
The idea behind this formation is easy to grasp as it is the fundamental
theme of maintaining a set position for as long as conditions allow, using
the remaining forces to harass the foe. Seeing that the grouping exists
already at the start there are no problems of setting up. There is also
nothing to stop both players from simultaneously employing this scheme.
This latter remark is both praise and indictment. While it is the ideal
defensive pattern, forestalling as it does most of the aggressive types of
formation, yet if both players adopt it at the same time then the play tends
to become very limited in scope. Unfortunately, under modern restrictive
styles this happens only too often, especially amongst the worshippers of
the drawn result. Ironically enough, this mid-game pattern is known to the
bookworms under the name of 'Pioneer'.
A characteristic of the play is the move G4 which comes early in the game,
making an E-line formation with extra supporting base. The opponent attacks
with the move D4, seeking exchanges to break it down; and the one who plays
this D4 first usually gains the initiative, for what it is worth here. A
typical example follows:
DIAGRAM 59
Scottish Championship, 1950.
White (Marshall)
+------------------------+
|::: w ::: w ::: w ::: |
| ::: w ::: w ::: :::|
|::: ::: w ::: w ::: w |
| b ::: w ::: ::: :::|
|::: ::: ::: b ::: w |
| b ::: b ::: b ::: :::|
|::: ::: b ::: b ::: |
| ::: b ::: b ::: b :::|
+------------------------+
Black (Oldbury) to play
The position is almost devoid of distinctive features and anything but a
drawn result would be a mild surprise. Black took the opportunity to play
D4 before White to which came the reply G2 (if instead, E5, C5, E5, then A5
and Black started to play along the A-line), A6, G4, and now the general
dissolution set in, thus: A4, G6, A4, D4, D6, C6, E4, E2, C4, B3, C2, D4
(bringing similar pressure on to Black, but it could not amount to much),
G2, A6, G4, B6, C3, A7, C5, E5, C5, A3, C7, B3, B2 - Drawn.
One could multiply instances of this type of play, without throwing a
great amount of new light upon it as by its strictly defensive character it
does not contain much variety of theme. All the same it is usually very
safe to adopt and practice in handling the formation will perhaps give the
student confidence to embark upon more ambitious schemes.
I have now dealt with all of the major themes of mid-game play, and you
are now sufficiently equipped in this field to approach it systematically,
so that you may attain conpetence and perhaps skill.
CHAPTER SEVEN
This is pure bunk
When I told you, in Chapter One, that it would not be best for me to begin
at the beginning you will see now that I had a point there.
It is now possible for us to survey together the problems of the opening.
Whilst the tenets of space, time, and force are as important here as at any
other stage of the game, yet we should bear in mind that we strive here
towards objectives of quite a different nature. Our concern is to arrive at
a position which can be assessed favourably in general terms, so enabling
us to enter the mid-game satisfied with our prospects. That is all we are
justly entitled to expect from the opening moves.
If our wish is to create a type of position that will favour us, then it
is evident that in this respect initiative is the key to success. We can
narrow the issue of how best to play the openings to one of initiative.
Consider the position in Diagram 60, which we must all face.
DIAGRAM 60
White
+------------------------+
|::: w ::: w ::: w ::: w |
| w ::: w ::: w ::: w :::|
|::: w ::: w ::: w ::: w |
| ::: ::: ::: :::|
|::: ::: ::: ::: |
| b ::: b ::: b ::: b :::|
|::: b ::: b ::: b ::: b |
| b ::: b ::: b ::: b :::|
+------------------------+
Black - to play
If you make all the usual counts in space, force, and time, you will find
equality in the first two elements named, and the slight advantage in time
to White based on the hypothesis that if there are no exchanges in the play
which follows then 'the move' will be against Black. All in all, there seems
a slight 'pull' in favour of White.
Yet everything has not been taken into account. You may recall that I
mentioned much earlier that time is manifested on different levels, and to
have the initiative is one way an advantage in time may be held. Black, with
the right to move first. so has the initiative.
It is rather interesting to ask which of these aspects of time is of
greater moment at this stage of the game. I will tell you that the advantage
of initiative in the opening far outweighs the disadvantage of a level time-
count, though it would be reckless to overstate the case - an alteration by
only two or three moves in development can be enough to swing the issue the
other way. Nevertheless, you may safely take it that when the counts are
level in the opening it is much better to possess the initiative.
Here is a short game which illustrates the point. Throughout this game,
White endeavours to capitalize on his advantage in development, by avoiding
exchanges and thus seeking a block position. He does this simply by copying
Black's moves, like this: A4, A4, C4, C4, F4, F4, C5, C5, C3, C3, F3, F3,
A2, A2, C4, C4, and now if Black were foolish enough to continue with A3
then White too would play A3 and soon win, in similar style to Diagram 25 -
another case where 'the move' alone wins. However, instead of this A3, Black
can exchange E3, C7, E3, and after White does the same, E3, C7, E3, we get
G4, A6, E6, G4, A6, E6, now Black moves D4 - and White has no reply; Black
will gain the White man at D3 and win the game. Thus, the initiative defeats
the level time-count.
Making the first move of the game is equivalent to serving in tennis or
leading in contract bridge. It has the same characteristic quality in that
when correctly employed it influences and determines the response of the
opposition. In draughts, it is equally incumbent upon Black to make the
first threats as it is upon White to find relevant replies to those threats.
If the Black player does not keep up the pressure then he wastes the natural
advantages of the opening and may allow White to gain the initiative. If,
instead of being content to reply to Black's threats until such time as the
pressure ceases, White goes off on a bat of his own, then he too will be
asking for trouble.
This does not imply that at every point of a game there is one particular
move and only one that answers the requirements of the situation, though
some players would have us believe differently. You will hear often some
such remark, 'When the top-notchers play, every move has to be made just so
- or else it is all over.' This is pure bunk. Very often, one has the
choice of several different moves, any of which will meet the needs of the
situation; it is also perfectly possible to construct varying plans from one
and the same position, each plan possessing its own merit. There are many
positions wherein it would be ludicrous to insist that any one move is
better than all others. Draughts is not all that precise, believe me.
DIAGRAM 61
White - to play
+------------------------+
|::: w ::: w ::: w ::: w |
| w ::: w ::: w ::: w :::|
|::: w ::: w ::: w ::: w |
| ::: ::: ::: :::|
|::: ::: b ::: ::: |
| b ::: ::: b ::: b :::|
|::: b ::: b ::: b ::: b |
| b ::: b ::: b ::: b :::|
+------------------------+
Black
In the opening, it is less important to compare the strength of various
lines of play than it is to appreciate that each may lead to a quite
dissimilar type of game. It is the variations in character which you must
come to understand.
If Black is to begin with a threat, then of course it may as well be of
some potency - the stronger it is, the less will White be able to afford to
ignore it. The threat of an A-line attack is almost always effective in the
opening, so Black may choose between D4 and B4 for this purpose. We may
observe that the former choice gives Black the extra prospect of a D-line
attack, by following up with the moves D3 then D2 - with D5 in view later.
Let us examine this initial D4 move and some of its consequences.
White has two immediate methods of meeting Black's threats; by an exchange
or by blocking Black's A-line with the move E4.
After an exchange (D4 or G4) it is to be observed that White gains an
amount of space in centre control. This is offset by the time-count, which
will stand at 21 for Black and 23 for White, a disadvantage to White at this
early stage, especially as Black keeps the initiative.
Both D4 and G4 are basic space-for-time exchanges, and you must understand
the mechanism of such exchanges as well as their effect on the succeeding
play.
You will note that, when the Black jump is made, White loses a man on his
fourth rank. When the White jump is made Black loses a man on his sixth
rank. Thus, the man Black loses is one which had advanced further than had
the White man, two ranks further in fact, and so after the exchange White is
2 moves ahead in development.
You should play through these exchanges several times so as to grasp this
idea thoroughly. It is necessary to realize the effect that any exchanges
will have on the time-count; if you understand the mechanism then you will
be able to ascertain their effect at the proper time - before the event, not
after.
In all such openings where a space-for-time exchange is made, the broad
strategy is much as you would expect it to be. Each side tries to increase
it's own advantage: the side which has gained space will try to build up an
imposing formation; the side which enjoys the 'pull' in time will play a
waiting game, avoiding exchanges, with the insidious threat of the pincer
movement often lurking. So, as far as one can generalize with safety: in
these space-for-time openings the side possessing the advantage in the time
element is to be preferred. Perhaps this is because an advantage in time, of
this sort and degree, carries with it an indirect threat to bring the game
to an abrupt termination, and in the not too distant future.
Returning to Diagram 61: if space-for-time in the opening is an unprofit-
able exchange then it may be said that White should not make it in that
case. Yet one should remember that Black began the game with an inherent
advantage and it was used in a proper manner, to make a direct attacking
threat. Therefore, no matter where White moves, that move cannot deprive
Black of his position. To condemn the exchange on those grounds would be to
ask too much of a single move.
Before leaving this topic, I will make the general distinction that
White's D4 trade will tend towards a fairly active game, with chances of
D-line manoeuvres for White and pincers for Black; the G4 trade will create
an E-line formation, safe but passive defence. It would be futile to argue
the superiority of one system over the other; it is simply a matter for
personal taste.
We come now to the reply E4 to Black's D4 move. See Diagram 62:
DIAGRAM 62
White
+------------------------+
|::: w ::: w ::: w ::: w |
| w ::: w ::: w ::: w :::|
|::: w ::: ::: w ::: w |
| ::: w ::: ::: :::|
|::: ::: b ::: ::: |
| b ::: ::: b ::: b :::|
|::: b ::: b ::: b ::: b |
| b ::: b ::: b ::: b :::|
+------------------------+
Black - to play
In making this move White, at least for the time being, prevents Black's
A-line attack from materializing; White also prepares to meet a D-line
attack with a pincer defence. So it may be said that White makes a
satisfactory reply in this E4, though of quite a different nature to the
previous idea under discussion.
Black may now consider whether to bring pressure against the White man at
E4, so that Black may thus indirectly renew his A-line attack; or he may
choose to launch an attack along the D-line. Both plans are of considerable
merit and there are in addition several ways in which either may be put
into operation.
An example of the first mentioned: B3, B4, B4, E3, G4, D3, G3, B5, E2, D2,
B3, F4, A6, G4, forming Diagram 63:
DIAGRAM 63
Match, 1858
White (M'Kerrow)
+------------------------+
|::: w ::: w ::: w ::: |
| ::: w ::: ::: w :::|
|::: ::: w ::: w ::: w |
| w ::: w ::: ::: :::|
|::: b ::: ::: b ::: w |
| b ::: b ::: b ::: b :::|
|::: b ::: ::: b ::: |
| b ::: ::: b ::: b :::|
+------------------------+
Black (Martins) to play
Black now mobilized his A-line attack with the move D4 and the game
continued F6, A6, F4, D4, E2, D2, F5, C5, E5, D3, F7, B3, E3, B4, B2, D5, D5,
A5, D3, G2, B4, G5, A5, G5, C5, B5, A2, A6, A3, G7, B3, B8, B4, neatly drawn.
An example of a D-line attack, from Diagram 62: E4, G6, A4, B4, G5, C5, D3,
E3, F2 (with the characteristic threat of D6), E2, D2; Black builds up to an
involved mid-game structure which contains winning chances.
Once more from Diagram 62: Black may prefer to play a move that will keep
open alternative possibilities without yet committing himself to a specific
line. In this event, Black can choose from D3 or G4, both good developing
moves which reinforce the centre. However, it must not be forgotten that it
is up to Black to retain the initiative and so these non-committal tactics
must not be carried on in lieu of an attack, but solely in preparation for
one.
White has other possible replies to Black's opening D4 move, of course.
These are B4 or C4 or A4. The first three named are purely passive replies,
awaiting events, and if anything they increase Black's scope. They are good
moves to use if one wishes to give a less experienced opponent extra rope
with which to tie himself in knots - the great nineteenth-century Master,
James Wyllie, will rank as probably the outstanding exponent of all time at
this style of play.
White's remaining alternative, A4, is of a very different order and we
will now examine it.
We notice firstly that White here makes a direct threat to bring about an
exchange of the space-for-time species, which would if realized favour
White. Then we see that White actually invites Black to -
DIAGRAM 64
White
+------------------------+
|::: w ::: w ::: w ::: w |
| w ::: w ::: w ::: w :::|
|::: w ::: ::: w ::: w |
| ::: ::: w ::: :::|
|::: ::: b ::: ::: |
| b ::: ::: b ::: b :::|
|::: b ::: b ::: b ::: b |
| b ::: b ::: b ::: b :::|
+------------------------+
Black - to play
embark on an A-line attack, intending then to counter-attack along the
D-line and break up the Black formation. In addition, White threatens
indirectly to begin a pincer movement should Black try to avoid the other
threats, by playing either B3 or D3. What is Black to do in such a situation?
Before anything else, we must affirm that by making threats in this manner
White has violated a fundamental principle of the opening. There is no
justification here for the aggressive play on the part of the second player,
and no matter how alluring such schemes appear the fact remains that White
is overplaying his hand. Black has no cause to panic and can soon demonstrate
which side has the better game.
We know from discussing the mid-game that a formation erected along the
D-line is not of any great strength, as the men at D1 and D2 are kept out of
play so long as the structure stands. Black's next move then will be D3,
thus fixing White's entire single corner side. White continues with A3 to
get in his pincer attack; then comes D2 (direct threat of A5), E4, and Black
immediately breaks the grip by G4, A6, G4, disclosing the coming attack
through the centre; then after B4, D5, B3, G6 White is very restricted and
Black's superior position is evident.
As we see that D4 is a good opening move for Black, it is reasonable to
conclude that it is good for White too, should Black open up with some other
move. It is especially favourable to White when it carries with it a direct
threat, as it does when played in reply to G4 or F4. By commencing with
either of these moves Black gives up the initiative, as he does also if he
begins with C4 - though in a different way. See Diagram 65.
DIAGRAM 65
Black
+------------------------+
|::: b ::: b ::: b ::: b |
| b ::: b ::: b ::: b :::|
|::: b ::: b ::: b ::: |
| ::: ::: ::: b :::|
|::: ::: ::: ::: |
| w ::: w ::: w ::: w :::|
|::: w ::: w ::: w ::: w |
| w ::: w ::: w ::: w :::|
+------------------------+
White - to play
A cardinal principle of opening play is that each side shall, where
expedient, develop rapidly the men which are in the single corner zones, as
these men stand nearest to the ememy - accepting the D diagonal as the line
which divides one army from the other. The motive behind an early C4 move is
precisely that; and it is to be followed up conditionally with either C5 or
B5, according to circumstances. The enemy will of course aim to prevent or
at least delay this mobilization.
Here, White plays F4 which is an important and characteristic reply as it
grips Black's advanced man. When Black then plays C3 so as to get in his own
C5 move, White intercepts this with G3 in an effort to tie up Black's single
corner altogether. Typical moves which may then follow are C2, A4, F4, A3,
C5, G5, A5, E5, C5, which form the position shown previously on Diagram 54.
Black has loosened the grip, but is now open to attack along the D-Line.
These remarks concerning an early C4 apply with even greater force to
White. In these cases Black, the attacker, is a move ahead and is usually
able to get a firm grip on the single corner before White can take adequate
preventive steps.
An exception to this is when Black begins his game with A4. Now C4 is a
powerful White reply; Black dare not play F4 here as it would not grip White
at all but allow an immediate C5 move and a good A-line attack in view for
White.
Returning to Diagram 65: we must note that Black fears the F4 move from
White only if it comes straightaway. For instance, if White replies D4 then
Black has time to prepare with C3 - or even E4. This latter is very interest-
ing. See Diagram 66.
DIAGRAM 66 DIAGRAM 67
Black Black
+------------------------+ +------------------------+
|::: b ::: b ::: b ::: b | |::: b ::: b ::: b ::: b |
| b ::: b ::: b ::: b :::| | b ::: ::: b ::: :::|
|::: b ::: ::: b ::: | |::: b ::: b ::: b ::: b |
| ::: b ::: ::: b :::| | ::: ::: ::: w :::|
|::: ::: w ::: ::: | |::: ::: ::: w ::: w |
| w ::: ::: w ::: w :::| | w ::: w ::: ::: :::|
|::: w ::: w ::: w ::: w | |::: ::: ::: w ::: w |
| w ::: w ::: w ::: w :::| | w ::: w ::: w ::: w :::|
+------------------------+ +------------------------+
White - to play White - to play
The position is comparable to that of Diagram 62, and White now plays F4,
to avoid similar play and to begin a manoeuvre to tie up Black's single
corner. It is worth recording that all the 'authorities' are of the opinion
that White can force a win from this point, no matter where Black plays, and
as a result this opening is 'barred' from respectable draughts society as
untenable.
Once again, an analysis by theory discloses the real truth of the situation
where all other efforts have failed. After White's F4 move Black can bring
about a swift but effective rearrangement of the elements thus: C5, E5, G6,
E4, C3, D3, A3, forming Diagram 67.
If you will analyse this situation in the way I have taught you, it will
become apparent that Black has given up an amount of force, so as to obtain
considerable gains in both space and time. Whilst in force Black has 10 men
against White's 11, in time he has an average development of 2 contrasted
with White's 2.45. Black has also an appreciable advantage in space, having
a fluid position in contrast to White's cramped double-corner men. In
addition there is a direct threat to play D4 and force an exchange that
would worsen White's development.
Black has every reason to be satisfied with his mid-game prospects.
It is not the aim of this chapter to catalogue all the possible ways of
opening your game. Many of these are merely duplications in theme of openings
we have discussed, and differ only in detail. Always it is the general prin-
ciple that you should grasp.
In Chapter Three, we set out upon a scientific enquiry into the game of
draughts. Much that was hitherto undefined and obscure is now clarified and
what is more, a vital study method has been enunciated - for the first time
in the entire history of the game.
You have seen what science can do. From here on the artist, the gambler,
and the philosopher take over. Enter beauty, bluff, and wit.
Before going further, I would strongly advise you to re-read from the
very beginning and then lay aside this book for perhaps a week, or more, so
as to give yourself time to absorb everything to date. Then we can go on
afresh.
B O O K 3
INTRODUCTION
Contrasts
'So weak and lacking in endurance is the human frame that if it pass from
one day to another without giving tribute to sleep it fails in strength for
anything it may wish to do until by means of this same rest it be restored
again. And not only must it satisfy itself with time for slumber, in order
to be able to continue in the round of our duties, it is further necessary to
sandwich in some means of recreation, in which the body rests and the mind
has delight without vacuity. For this restorative effect we have games, which
however are not to be made a habit or a continuous employment (as in our time
we see) in following which, as though they cultivated it, men go on to
discover a thousand tricks and sophistical inventions to usurp the silver
of those with whom they play - games like cards and several others. From all
this our game of draughts is free; instead of luck we are indeed helped to
acquire caution; while it is legitimate, spirited and ingenious. And it not
only serves as a recreation to man; it also carries its doctrine. It
represents a player as a general who guides and administers an army, who
sets it against an equal opponent, and by his good leading and resource is
able to destroy the other's forces and consummate the victory'
Lorenzo Valls, 1597
'When the other moves, indeed at all times, watch well his hands that no
false moves are made; such as if he moves over two squares at a time, or
make two moves in succession, or sideways or backwards with an ordinary man,
or when he pretends to move and yet leaves the piece in its old position; or
when in moving he puts back another man with his fingers under cover of his
hand; or makes moves with both hands at a time. Again in taking he may
remove the wrong man; or more men than he ought, or men he cannot justly
reach. When he ought to crown see that he does not put back a man, either of
his own or ours, or sneak off with one of ours, and replace by one of his.
When moving see that he does not conceal some other piece which ought to
take, so that he can miss this and not be huffed for it. See that he does
not make a cloud with his tobacco smoke, so that we do not see what we
ought to see. It is necessary to hold out for correct practice. Then
frequently count over the men on both sides, and mark their place, both on
which side there is the advantage, and on which there is a danger. See that
the opponent does not keep a hand resting on the board, far less both hands.
Do not move till his hands are quite clear of the board.'
'F.T.V,' c.1702.
CHAPTER EIGHT
Set to Music
You sit at the table and you hold the coin ready. He faces you and the first
game of the match will soon begin. His cronies stand around to watch their
club champion in action. but neither he nor they know what is in store.
You toss the coin, he calls 'heads', and it is. He chooses White and you
try not to laugh out loud. This is for the best in three games and he
chooses White! You may as well pick up the money now; the champion was
surely right to insist on playing for a stake, you will endorse that every
time.
The game starts: you move D4, and he replies B4; you decide to come with
the A-line attack, but later, and so you play D3.
You are glad you did that when he takes the cut by C5, G5, A5, E5, C5, as
you know your superiority along the D-line will soon undermine his isolated
man. Perhaps he too begins to realize his difficulties, because when you
continue D2 he plays B3 to bring across extra support and enable him to meet
your next move A3, with B4.
Your A-line attack is now taking shape and by bringing pressure against
White's man at C5 you can hasten the process - so you play F2, forcing E2.
This is even easier than you thought it would be. You almost feel sorry
for him, but you remind yourself that this is your long-awaited hour. You
see that all you have to do is take a man on to C5 and then follow with F3,
and he can do nothing about it.
You do not move for a while, as you wish to enjoy this moment. The
worried looks of his supporters are a sight to see - though you have to
admit the champion shows nothing. You wonder what it feels like to be an
ex-champion. When the crowd ask you later how you won the title you will
lower your eyes modestly and say that you guess it was just luck - that is
always the most crushing way to get your own back.
At last you move, B4 He must resign in a very little while.
DIAGRAM 68
Study by Oldbury
Black
+------------------------+
|::: b ::: ::: b ::: |
| b ::: b ::: b ::: b :::|
|::: ::: b ::: ::: b |
| ::: w ::: b ::: b :::|
|::: w ::: ::: ::: |
| ::: ::: ::: w :::|
|::: w ::: w ::: w ::: w |
| w ::: ::: w ::: w :::|
+------------------------+
White - to play
The champion gives a sort of sigh and looks across at you, perhaps more in
sorrow than in anger. He moves A6.
Of course he is just throwing away the game, so as to come out with the
old alibi, 'Oh dear me, what a silly mistake; but for that I would have won
easily - of course.' As you jump the three men, E8, you wonder how low
anyone can get. He plays F4.
Then it hits you.
Your nerves are still good so you do not say a word, though back of the
crowd someone starts to whistle 'Out of Nowhere'. You reset the men for the
second game, and your opponent has the Blacks. He tees off with your move,
D4.
You are going to be very careful this time. You play E4, and after that
you reply to G4 with B4. You know some good tunes, too, and under your
breath you murmur 'Ashes to ashes, dust to dust; if the A-line don't get him
the pincers must.'
The game proceeds D3, D3, F3, B5, F2, D2, D2 and he is playing right into
your hands. You apply the clamp with B4, G5, B3, B4, C5 (nobody foresaw
this, you are sure), C6, B2, E5, C5 and now let him look for a good move
(see Diagram 69).
He sits there, very quiet and rather sad. You look towards the exit. You
know it can't happen twice, and yet he moves C4.
This gives you a choice of jumps, E6 or G6. You study long and hard. The
whistler is heard in a sinister off-key version of 'Again'.
DIAGRAM 69
Study by Sturges
White
+------------------------+
|::: w ::: ::: w ::: |
| w ::: w ::: w ::: w :::|
|::: w ::: b ::: w ::: |
| ::: ::: b ::: :::|
|::: ::: b ::: w ::: w |
| b ::: ::: ::: b :::|
|::: b ::: b ::: b ::: b |
| ::: b ::: ::: b :::|
+------------------------+
Black - to play
On your way home you try to work out what went wrong. You refuse to
believe you did not play according to theory; each one of your moves was
motivated by the principles which you have so religiously imbibed. Yet your
opponent was not only able to brush aside your schemes, but with the most
fantastic moves. You determine to waste no more time on this science fiction
of a system. You will tear it up or, better still, sell it to someone you
wish to beat.
Perhaps this is where I had better cut in. You have just met artistry in
draughts.
We have become familiar with a method of assessing positions by analysing
the individual parts and then summarizing them and forming a plan of action.
This we are able to do to a very high degree of precision. Yet the real
value of a position will depend on its total effect, which can be ascert-
ained by the scientific method in the vast majority of cases - but not all.
At times, the decisive factor is not to be found in a strictly measurable
form - because it consists solely of the peculiar relationship between
pieces at a given moment.
A simple parallel may be found in the realm of music. Anyone who has
studied sound production can tell you the exact frequency of the air
vibrations which are set up when you strike a note on a piano, and can tell
you that if you strike another note just one octave higher, then the rate of
vibrations will be exactly double that of the first. This is science. Yet if
you strike three or four notes all at once, then the only difference between
a chord and a discord will be - not the total rate of vibrations set up -
but the effect that they have on the listener. One could study harmonic
progressions a lifetime yet still not be a Claude Debussy. It is the union
of notes that makes the chord, and it is the combining of factors in
draughts play that creates the artistic coup.
Thus conceding the value of creative talent - if one could not assess even
the likely presence of a coup, except by intuitive means, then the value of
a scientific method would be almost nil. A player would never be able to
trust to his positional judgment for fear of walking into some hidden snare.
Luckily, there are signs which can at least warn us of possible danger.
All positional play operates in the elements of space and time, and gains
in the third element, force, are the result of gains made in the other
elements. However, all combinative play operates in the element of force
alone. Here, gains in any or all of the elements come as the result of the
use of force. The element of force can be invoked in two ways, both of which
may override all other considerations. These are easy to demonstrate, as
follows.
Begin a game with the move C4 and reply with G4. White threatens to gain a
man and Black's choice of moves is straightaway restricted by this threat.
Whilst considerations of space or time factors may govern his selection from
either C3 or B5, any other move is out of the question. In this way White
uses compulsion, operating in the element of force.
The value of such tactics will depend on whether the threat can be
combined in some way with other threats. Several threats posed all at once
can rarely be adequately met. In the instance just shown, after Black moves,
White is unable to follow up with an effective threat and so the previous
effort amounts to very little.
From the beginning again, play C4, and vary with B4, then F4. White here
is able to combine his former threat with another method of compulsion - by
playing G4. White compels Black to jump F6, whereupon E6 will win for White
two men for the price of one. So, while Black meets his obligation to jump
he cannot at the same moment protect himself from the threat made by White's
G4 move.
If you dwell on this for a while, you will come to see that such manoeuvres
can occur only when opposing pieces are in close proximity to each other.
One piece can only compel another if they are in contact, and these points
of contact can alone form the basis of any combinative series of moves.
It is easy to see that where a position is wide open, so to speak, and it
is not possible to compel the opponent then no combinative play will be 'on'.
The interesting feature of the two games which led to Diagram 68 and
Diagram 69 is that all the moves made by the side which lost were logical
and in terms of space and time, perfectly sound. This is the essemce of all
traps. I would like to bring out this point. If there is no bait there is no
trap. The game: C4, B4, F4, G4 is not a trap because there is no reason why
Black should play into that situation. The game demonstrates an indirect
threat, and no more.
In playing the game discussed in Chapter Six at Diagram 56, I did
entertain the hope that the following might arise out of it:
DIAGRAM 70
Study by Oldbury
White - to play
+------------------------+
|::: ::: ::: ::: |
| w ::: w ::: w ::: w :::|
|::: w ::: ::: ::: w |
| w ::: ::: b ::: b :::|
|::: ::: b ::: b ::: |
| w ::: b ::: b ::: b :::|
|::: ::: b ::: ::: |
| ::: ::: ::: :::|
+------------------------+
Black
Though Black poses a direct threat to gain a two-for-one exchange, this
would leave behind so many exposed men that White may feel justified in
going straightaway for a King in order to counter-attack from the rear. The
consensus of expert opinion supports that view at any rate, for this
position has cropped up on several occasions during competitive play and
each time the White player has continued by E7. This move has led to a win
for White - yet I will show you that this is an illusion and that in making
this move White places himself in jeopardy, if only the Black player has the
wit to see it.
After their E7 move, I play F6 and then comes B4, F4, D3, D7, E8, F6, E7,
E8, A3, C7, E4, D7, E5, C6 (with the threat to move C5 and White would never
regain his lost piece), G4, A6, G7, G(6)5, G4, B3 (climax), F7, E5, C5, B3,
to a Black win.
You will observe how the pressure is maintained throughout - because, once
Black has won material, White is obliged to try to get it back, and these
efforts only serve to lead White along the desired route. This is one of the
most vital principles of play in the element of force and you will do well to
grasp its implications firmly.
Fron Diagram 70, the proper play for White is A3, G7, D3, F4, and now E7
is in order and leads to a good draw. This too is a little combination.
The following merits special attention.
A D-line attack seems the logical procedure here for White. One takes into
account also that after the move D5 Black could not play B3, to start a
pincer movement, because of the devastating trap by B4. Who can deny the
power of the White position.
DIAGRAM 71
Study by Anderson
White - to play
+------------------------+
|::: w ::: w ::: w ::: |
| ::: w ::: w ::: w :::|
|::: ::: w ::: w ::: w |
| ::: w ::: w ::: :::|
|::: b ::: ::: b ::: |
| b ::: ::: ::: b :::|
|::: b ::: b ::: b ::: b |
| ::: b ::: b ::: b :::|
+------------------------+
Black
So D5 is played, and hopes are high. The next few moves are what one would
expect, thus: B5, D4, B3, B3, B4, E2, E2, F3, B7, F3, B5; and now it is a
trifle disturbing to note there is no profit for White in B4 (as perhaps had
been intended) and so White plays instead A2 - and surely this will be good
enough? The D-line attack is now under way and must soon break through.
Rather surprisingly, Black meekly allows White full sway and the game
continues E3, D6, D4, D6, F4, D4, G3, D7, B2, E8, F5 - and the awful truth
is disclosed!
White now has only E7, after which Black executes a paralysing coup by F6,
B4, C4, E6, and B3 demolishes White utterly.
If you carefully go over the play from Diagram 71, step by step, you will
see that Black has most cunningly led White to his doom, and that after his
inviting D5 move White was, in fact, lost. You will benefit a great deal by
studying this.
It is worth recalling that Anderson defeated Wyllie with this same coup in
their World Championship match of 1847. If I had to select but a single
example of the very best in draughts play then this would be it.
The kind of skill displayed here is what is often called 'genius' and IS a
rare talent. Nevertheless it may be developed just as may any other faculty,
by practice and appropriate exercise.
Undoubtedly the best way to gain skill in executing the artistic coup is
by the study and appreciation of draughts problems. Let us explore the
subject.
CHAPTER NINE
And rubric to you
A draughts problem is a composed study in the element of force. It is a
separate species, distinct from end-game studies in that it does not employ
the concepts of space or time and is not to be solved by planning from
theoretical principles.
It is an exercise in visualization, and is solved by identifying points of
contact and relating them to one another. The solution is simply the chain
of threats, direct or indirect, which enforces the terms of the problem.
The value of problem study is immense, in that it teaches one to be
observant of detail and in that it flexes the imaginative powers.
To many, composing draughts problems equals in fascination the playing of
the game and it is indeed a rewarding field of activity. Just as there are
playing techniques, so in composing are there priciples of construction. By
this I mean there are essential features, in the absence of which no problem
can be rated a worth-while production, be it ever so spectacular.
There are three vital tenets. Firstly: a problem is always an essay in
force. Secondly: a problem has only one solution. Thirdly: a problem employs
no more than that number of pieces needed to execute its theme.
The presence of these purely mechanical attributes, though essential, does
not in itself make a good problem, which in addition expresses wit, profund-
ity, and charm. Yet a problem has no wit if its solution rambles on through
long-winded variations which should properly be set in end-game studies; it
is not profound if there are three or four ways of solving it or if the
moves of the solution can be played in any order; it lacks charm if it has
in it extra pieces which do nothing save act as patches to hide threadbare
themes or if the solution commences with an exchange - taking off pieces
that had no bearing on the real action.
To end this book, I present a selection from my own problem compositions.
I have tried to arrange these more or less in order of difficulty, though
you may find none of them exactly easy. If they were easy then you would
achieve little by solving them.
In those cases wherein the terms of the problem call for a drawn result,
I assume it is understood that here the task is to prevent the enemy from
making a decisive gain of material. The play is still in the element of
force.
I do not show the solutions to these problems. All of them end in a very
clear-cut manner, and you will know when you have mastered them.
Good hunting!
PROBLEMS BY OLDBURY
1 2
White White
+------------------------+ +------------------------+
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: w ::: ::: :::| | ::: w ::: B ::: :::|
|::: ::: ::: w ::: w | |::: ::: ::: ::: |
| w ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: b ::: ::: b | |::: ::: ::: B ::: w |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: b ::: | |::: ::: ::: ::: |
| ::: b ::: ::: :::| | ::: b ::: W ::: :::|
+------------------------+ +------------------------+
Black to play and win Black to play and win
3 4
White - to play White
+------------------------+ +------------------------+
|::: w ::: ::: ::: | |::: w ::: ::: ::: |
| w ::: ::: ::: :::| | ::: ::: ::: :::|
|::: b ::: ::: ::: b | |::: ::: ::: ::: |
| ::: b ::: W ::: :::| | ::: ::: ::: w :::|
|::: ::: ::: ::: | |::: b ::: b ::: ::: |
| ::: ::: ::: :::| | ::: ::: b ::: :::|
|::: ::: ::: ::: | |::: ::: ::: W ::: |
| b ::: ::: ::: :::| | ::: ::: ::: b :::|
+------------------------+ +------------------------+
Black - to win Black to play; what result?
5 6
White White
+------------------------+ +------------------------+
|::: ::: B ::: ::: W | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: w ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: b ::: ::: ::: | |::: ::: ::: ::: |
| ::: b ::: ::: w :::| | B ::: ::: ::: :::|
|::: ::: W ::: ::: | |::: W ::: ::: B ::: |
| ::: ::: ::: :::| | ::: W ::: ::: B :::|
+------------------------+ +------------------------+
Black to play; what result? Black to play and win
7 8
White White to play and draw
+------------------------+ +------------------------+
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: w ::: ::: :::| | ::: w ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: B ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: B ::: B ::: W :::| | ::: B ::: ::: W :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| B ::: ::: W ::: :::| | B ::: W ::: ::: :::|
+------------------------+ +------------------------+
Black to play and win Black
9 10
White White
+------------------------+ +------------------------+
|::: W ::: B ::: ::: | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
|::: B ::: w ::: ::: B | |::: ::: ::: W ::: b |
| ::: ::: W ::: :::| | ::: ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: b |
| ::: ::: B ::: :::| | b ::: B ::: ::: :::|
|::: ::: ::: ::: | |::: ::: ::: ::: |
| ::: ::: W ::: :::| | W ::: W ::: ::: :::|
+------------------------+ +------------------------+
Black to play and win Black to play; what result?
11 12
White White
+------------------------+ +------------------------+
|::: ::: ::: w ::: w | |::: ::: ::: ::: B |
| w ::: ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: b ::: b | |::: w ::: ::: b ::: w |
| b ::: b ::: ::: :::| | w ::: ::: b ::: :::|
|::: ::: ::: ::: | |::: ::: b ::: ::: |
| W ::: b ::: b ::: :::| | ::: b ::: ::: :::|
|::: ::: ::: ::: W | |::: ::: ::: ::: |
| ::: ::: ::: :::| | ::: ::: ::: W :::|
+------------------------+ +------------------------+
Black to play; what result? Black to play and win
13 14
White White
+------------------------+ +------------------------+
|::: ::: ::: ::: | |::: ::: B ::: ::: w |
| b ::: w ::: ::: :::| | ::: ::: ::: :::|
|::: ::: ::: b ::: | |::: B ::: ::: b ::: |
| ::: ::: ::: B :::| | ::: ::: b ::: B :::|
|::: ::: ::: b ::: W | |::: ::: W ::: ::: |
| W ::: ::: ::: :::| | ::: ::: ::: W :::|
|::: W ::: b ::: ::: | |::: b ::: W ::: ::: W |
| ::: ::: ::: :::| | ::: ::: ::: :::|
+------------------------+ +------------------------+
Black to play and win Black to play and win
15 16
White White
+------------------------+ +------------------------+
|::: ::: ::: ::: | |::: w ::: ::: ::: |
| ::: b ::: w ::: :::| | ::: ::: ::: :::|
|::: ::: w ::: ::: w | |::: b ::: ::: ::: w |
| ::: ::: ::: w :::| | ::: b ::: b ::: b :::|
|::: ::: ::: b ::: w | |::: ::: b ::: b ::: |
| ::: ::: b ::: b :::| | ::: W ::: ::: b :::|
|::: ::: W ::: b ::: | |::: ::: w ::: b ::: |
| W ::: b ::: ::: b :::| | ::: W ::: W ::: :::|
+------------------------+ +------------------------+
Black to play and draw Black to play; what result?
17 18
White White
+------------------------+ +------------------------+
|::: w ::: ::: w ::: | |::: w ::: ::: w ::: |
| ::: b ::: w ::: :::| | ::: ::: ::: :::|
|::: ::: b ::: ::: w | |::: B ::: b ::: b ::: w |
| W ::: b ::: b ::: :::| | w ::: ::: ::: :::|
|::: ::: b ::: b ::: w | |::: b ::: b ::: b ::: w |
| ::: b ::: b ::: :::| | ::: b ::: b ::: b :::|
|::: W ::: w ::: b ::: | |::: w ::: W ::: W ::: |
| ::: ::: ::: :::| | ::: ::: ::: :::|
+------------------------+ +------------------------+
Black to play and win Black to play and win
19 20
White White
+------------------------+ +------------------------+
|::: w ::: ::: w ::: | |::: ::: ::: B ::: w |
| W ::: ::: b ::: :::| | w ::: ::: b ::: :::|
|::: b ::: b ::: b ::: b | |::: b ::: b ::: ::: |
| ::: W ::: ::: b :::| | ::: b ::: b ::: b :::|
|::: ::: b ::: b ::: W | |::: W ::: w ::: b ::: w |
| ::: ::: b ::: w :::| | ::: ::: W ::: b :::|
|::: ::: w ::: W ::: b | |::: ::: w ::: b ::: |
| ::: ::: ::: :::| | ::: ::: ::: W :::|
+------------------------+ +------------------------+
Black to play and win Black to play and win
21 22
White White
+------------------------+ +------------------------+
|::: ::: w ::: B ::: | |::: B ::: w ::: ::: w |
| ::: B ::: ::: B :::| | ::: B ::: ::: w :::|
|::: b ::: ::: ::: | |::: B ::: b ::: ::: |
| w ::: b ::: W ::: :::| | W ::: b ::: ::: b :::|
|::: b ::: W ::: W ::: b | |::: W ::: W ::: ::: |
| ::: b ::: ::: b :::| | w ::: ::: ::: :::|
|::: W ::: ::: ::: W | |::: ::: ::: b ::: |
| ::: ::: ::: :::| | ::: W ::: b ::: :::|
+------------------------+ +------------------------+
Black to play and win Black to play; what result?